Alerts
Wishlist
Cart
Sign In
Categories
Current Affairs & GK
Current Affairs
Show All Current Affairs & GK
eBooks
General Aptitude
Arithmetic Aptitude
Data Interpretation
Show All General Aptitude
General Knowledge
Basic General Knowledge
General Science
Show All General Knowledge
Medical Science
Anatomy
Biochemical Engineering
Biochemistry
Biotechnology
Microbiology
Show All Medical Science
Technical
Database
Digital Electronics
Electronics
Networking
Show All Technical
Verbal and Reasoning
Logical Reasoning
Verbal Ability
Verbal Reasoning
Show All Verbal and Reasoning
›
For the equation x² + 4x + k = 0 to have real roots, what must be the minimum va
For the equation x² + 4x + k = 0 to have real roots, what must be the minimum value of k? (2023)
Expand All
Collapse All
Practice Questions
1 question
Q1
For the equation x² + 4x + k = 0 to have real roots, what must be the minimum value of k? (2023)
-4
0
4
8
Show Solution
Copy
The discriminant must be non-negative: 4² - 4*1*k ≥ 0, thus k ≤ 4.
Questions & Step-by-step Solutions
1 item
Q
Q: For the equation x² + 4x + k = 0 to have real roots, what must be the minimum value of k? (2023)
Solution:
The discriminant must be non-negative: 4² - 4*1*k ≥ 0, thus k ≤ 4.
Steps: 10
Show Steps
Step 1: Identify the equation given, which is x² + 4x + k = 0.
Step 2: Recognize that for a quadratic equation to have real roots, the discriminant must be non-negative.
Step 3: The discriminant (D) for the equation ax² + bx + c = 0 is given by the formula D = b² - 4ac.
Step 4: In our equation, a = 1, b = 4, and c = k.
Step 5: Substitute the values into the discriminant formula: D = 4² - 4*1*k.
Step 6: Simplify the expression: D = 16 - 4k.
Step 7: Set the discriminant greater than or equal to zero for real roots: 16 - 4k ≥ 0.
Step 8: Rearrange the inequality to find k: 16 ≥ 4k.
Step 9: Divide both sides by 4: 4 ≥ k.
Step 10: This means k must be less than or equal to 4, so the minimum value of k for real roots is k ≤ 4.
Related Questions
F
Find the value of 5! (5 factorial). (2019)
Question: Find the value of 5! (5 factorial). (2019)Options: 12010015090Correct Answer: 120Solution:..
W
What is the value of (3 + 5) × (2 - 1)? (2020)
Question: What is the value of (3 + 5) × (2 - 1)? (2020)Options: 816106Correct Answer: 8Solution: (3..
I
If the roots of the equation x² + 7x + p = 0 are -3 and -4, find the value of p.
Question: If the roots of the equation x² + 7x + p = 0 are -3 and -4, find the value of p. (2019)Opt..
W
What is the value of the discriminant for the equation 3x² + 6x + 2 = 0? (2020)
Question: What is the value of the discriminant for the equation 3x² + 6x + 2 = 0? (2020)Options: 04..
I
If the roots of the equation x² + 5x + 6 = 0 are a and b, what is the value of a
Question: If the roots of the equation x² + 5x + 6 = 0 are a and b, what is the value of a + b? (201..
‹
Biology (School & UG)
Chemistry (School & UG)
Civil Engineering
Commerce & Accountancy
Computer Science & IT
Current Affairs & GK
Data Structures & Algorithms
eBooks
Electrical & Electronics Engineering
English (School)
General Aptitude
General Knowledge
General Knowledge & Current Affairs
Languages & Literature
Law & Legal Studies
Major Competitive Exams
Mathematics (School)
Mechanical Engineering
Medical Science
Physics (School & Undergraduate)
Quantitative Aptitude & Reasoning
Social Science (School)
Technical
Verbal and Reasoning
Vocational & Skill Development
›
Soulshift Feedback
×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy
?
0
1
2
3
4
5
6
7
8
9
10
Not likely
Very likely
✕
↑
