Q. If the roots of the equation x² + 2x + k = 0 are 1 and -3, what is the value of k? (2020)
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Solution
Using the sum and product of roots: 1 + (-3) = -2 and 1 * (-3) = -3, thus k = 3.
Correct Answer:
C
— 3
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Q. If the roots of the equation x² + 2x + k = 0 are real and distinct, what is the condition for k? (2020)
A.
k > 1
B.
k < 1
C.
k > 4
D.
k < 4
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Solution
The discriminant must be greater than zero: 2² - 4*1*k > 0, which simplifies to k < 1.
Correct Answer:
C
— k > 4
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Q. If the roots of the equation x² + 5x + 6 = 0 are a and b, what is the value of a + b? (2019)
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Solution
The sum of the roots is given by -b/a = -5/1 = -5.
Correct Answer:
A
— 5
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Q. If the roots of the equation x² + 5x + k = 0 are -2 and -3, find k. (2020)
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Solution
Using the product of roots: k = (-2)(-3) = 6.
Correct Answer:
A
— 6
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Q. If the roots of the equation x² + 5x + k = 0 are 1 and 4, find k. (2020)
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Solution
Using the sum and product of roots: k = 1*4 = 4, and sum = 1 + 4 = 5, thus k = 7.
Correct Answer:
D
— 7
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Q. If the roots of the equation x² + 5x + k = 0 are real and distinct, what is the condition for k? (2020)
A.
k > 25
B.
k < 25
C.
k = 25
D.
k ≤ 25
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Solution
The discriminant must be greater than zero: 5² - 4*1*k > 0, thus k < 25.
Correct Answer:
A
— k > 25
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Q. If the roots of the equation x² + 5x + q = 0 are 1 and 4, find q. (2019)
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Solution
Using the product of roots: q = 1 * 4 = 4.
Correct Answer:
A
— 5
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Q. If the roots of the equation x² + 7x + k = 0 are -3 and -4, find k. (2022)
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Solution
Using the sum of roots (-3 + -4 = -7) and product of roots (-3*-4 = 12), we find k = 12.
Correct Answer:
A
— 12
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Q. If the roots of the equation x² + 7x + k = 0 are 1 and 6, what is the value of k? (2020)
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Solution
Using the product of roots, k = 1*6 = 6.
Correct Answer:
C
— 8
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Q. If the roots of the equation x² + 7x + p = 0 are -3 and -4, find p. (2019)
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Solution
Using the sum of roots (-3 + -4 = -7) and product of roots (-3*-4 = 12), we find p = 12.
Correct Answer:
A
— 12
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Q. If the roots of the equation x² + 7x + p = 0 are -3 and -4, find the value of p. (2019)
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Solution
Using the product of roots: p = (-3)(-4) = 12.
Correct Answer:
A
— 12
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Q. If the roots of the equation x² + 7x + p = 0 are -3 and -4, what is the value of p? (2019)
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Solution
Using the product of roots: p = (-3)(-4) = 12.
Correct Answer:
A
— 12
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Q. If the roots of the equation x² + mx + n = 0 are 1 and -1, find m and n. (2020)
A.
0, 1
B.
2, 1
C.
0, 0
D.
1, 1
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Solution
The sum of the roots is 0 (m = 0) and the product is -1 (n = 1).
Correct Answer:
A
— 0, 1
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Q. If the roots of the equation x² + px + 12 = 0 are 3 and 4, find p. (2020)
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Solution
Using the sum of the roots: p = -(3 + 4) = -7.
Correct Answer:
A
— -7
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Q. If the roots of the equation x² + px + 12 = 0 are 3 and 4, what is the value of p? (2020)
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Solution
The sum of the roots is -p = 3 + 4 = 7, hence p = -7.
Correct Answer:
A
— -7
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Q. If the roots of the equation x² + px + q = 0 are 3 and -2, what is the value of p? (2019)
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Solution
Using the sum of roots formula, p = -(3 + (-2)) = -1, hence p = -1.
Correct Answer:
C
— 5
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Q. If the roots of the equation x² - 6x + p = 0 are 2 and 4, what is the value of p? (2023)
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Solution
The product of the roots gives p = 2 * 4 = 8.
Correct Answer:
B
— 12
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Q. The quadratic equation x² + 4x + 4 = 0 has how many distinct roots? (2021)
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Solution
The discriminant is 4² - 4*1*4 = 0, indicating one distinct root.
Correct Answer:
B
— 1
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Q. The roots of the equation x² + 2x + k = 0 are real and distinct if k is: (2020)
A.
< 1
B.
≥ 1
C.
≤ 1
D.
> 1
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Solution
For real and distinct roots, the discriminant must be positive: 2² - 4*1*k > 0, which simplifies to k < 1.
Correct Answer:
A
— < 1
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Q. The roots of the equation x² + 4x + 4 = 0 are: (2020)
A.
-2 and -2
B.
2 and 2
C.
0 and 4
D.
1 and 3
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Solution
The equation can be factored as (x + 2)² = 0, giving the double root x = -2.
Correct Answer:
A
— -2 and -2
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Q. The roots of the equation x² + 4x + k = 0 are 2 and -6. What is the value of k? (2021)
A.
-12
B.
-8
C.
-10
D.
-14
Show solution
Solution
Using the product of roots: k = 2 * (-6) = -12. The sum is 2 + (-6) = -4, which matches.
Correct Answer:
B
— -8
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Q. The roots of the equation x² - 8x + k = 0 are 4 and 4. Find k. (2021)
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Solution
Using the product of roots: k = 4 * 4 = 16.
Correct Answer:
A
— 16
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Q. What are the roots of the equation 3x² - 12x + 12 = 0? (2019)
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Solution
Dividing the equation by 3 gives x² - 4x + 4 = 0, which factors to (x - 2)² = 0, hence the root is 2.
Correct Answer:
B
— 4
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Q. What are the roots of the equation x² - 2x - 8 = 0? (2022)
A.
-2 and 4
B.
2 and -4
C.
4 and -2
D.
0 and 8
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Solution
Factoring gives (x - 4)(x + 2) = 0, hence the roots are 4 and -2.
Correct Answer:
C
— 4 and -2
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Q. What are the roots of the equation x² - 5x + 6 = 0? (2021)
A.
1 and 6
B.
2 and 3
C.
3 and 2
D.
0 and 5
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Solution
The roots can be found using the factorization method: (x - 2)(x - 3) = 0, hence the roots are 2 and 3.
Correct Answer:
B
— 2 and 3
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Q. What is the discriminant of the equation 3x² - 12x + 12 = 0? (2023)
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Solution
The discriminant is b² - 4ac = (-12)² - 4*3*12 = 144 - 144 = 0.
Correct Answer:
A
— 0
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Q. What is the discriminant of the equation 3x² - 12x + 9 = 0? (2023)
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Solution
The discriminant is b² - 4ac = (-12)² - 4*3*9 = 0.
Correct Answer:
A
— 0
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Q. What is the discriminant of the equation 4x² - 12x + 9 = 0? (2019)
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Solution
The discriminant is b² - 4ac = (-12)² - 4*4*9 = 144 - 144 = 0.
Correct Answer:
A
— 0
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Q. What is the discriminant of the equation x² + 6x + 9 = 0? (2020)
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Solution
The discriminant is b² - 4ac = 6² - 4*1*9 = 0.
Correct Answer:
A
— 0
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Q. What is the nature of the roots of the equation x² + 2x + 5 = 0? (2023)
A.
Real and distinct
B.
Real and equal
C.
Complex
D.
None of the above
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Solution
The discriminant D = 2² - 4*1*5 = 4 - 20 = -16, which indicates complex roots.
Correct Answer:
C
— Complex
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Showing 31 to 60 of 79 (3 Pages)
Quadratic Equations MCQ & Objective Questions
Quadratic equations are a fundamental part of mathematics that students encounter in their academic journey. Mastering this topic is crucial for excelling in school exams and competitive tests. Practicing MCQs and objective questions on quadratic equations not only enhances your understanding but also boosts your confidence, enabling you to score better in exams.
What You Will Practise Here
Understanding the standard form of quadratic equations.
Identifying roots using the quadratic formula.
Factoring quadratic equations and solving them.
Graphical representation of quadratic functions.
Applications of quadratic equations in real-life problems.
Discriminant and its significance in determining the nature of roots.
Common word problems related to quadratic equations.
Exam Relevance
Quadratic equations are a staple in various examinations, including CBSE, State Boards, NEET, and JEE. Students can expect questions that require them to solve equations, analyze graphs, and apply concepts to real-world scenarios. Common question patterns include multiple-choice questions, fill-in-the-blanks, and problem-solving tasks that test both conceptual understanding and application skills.
Common Mistakes Students Make
Confusing the signs when applying the quadratic formula.
Overlooking the importance of the discriminant in determining the nature of roots.
Failing to check for extraneous solutions after solving equations.
Misinterpreting word problems that involve quadratic equations.
FAQs
Question: What is the standard form of a quadratic equation?Answer: The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants, and a ≠ 0.
Question: How do I find the roots of a quadratic equation?Answer: You can find the roots using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).
Now is the time to enhance your skills! Dive into our practice MCQs on quadratic equations and test your understanding. Remember, consistent practice is key to mastering this topic and achieving success in your exams!
