Q1. What is the solution to the quadratic equation x^2 + 6x + 9 = 0?
Solution:
The equation x^2 + 6x + 9 can be factored as (x + 3)(x + 3) = 0. Thus, the solution is x = -3.
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Q2. What is the sum of the roots of the equation x^2 + 6x + 9 = 0?
Solution:
The sum of the roots can be found using -b/a. Here, b = 6 and a = 1, so the sum is -6.
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Q3. Which of the following is a factor of x^2 - 9?
Solution:
x^2 - 9 is a difference of squares and can be factored as (x - 3)(x + 3).
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Q4. Which of the following represents the quadratic equation with roots 1 and -3?
Solution:
Using the roots, we can write the equation as (x - 1)(x + 3) = 0, which expands to x^2 + 2x - 3 = 0.
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Q5. What is the value of x in the equation 5x + 3 = 18?
Solution:
To solve 5x + 3 = 18, subtract 3 from both sides: 5x = 15. Then divide by 5: x = 3.
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Q6. What is the solution set for the equation x^2 - 9 = 0?
Solution:
Factoring gives (x - 3)(x + 3) = 0. Thus, the solutions are x = 3 and x = -3.
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Q7. What is the solution set for the equation 3x + 4 = 10?
Solution:
To solve 3x + 4 = 10, subtract 4 from both sides: 3x = 6. Then divide by 3: x = 2.
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Q8. What is the factored form of the polynomial x^2 - 6x + 9?
Solution:
The polynomial x^2 - 6x + 9 can be factored as (x - 3)(x - 3) or (x - 3)^2.
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Q9. What is the vertex of the parabola represented by y = x^2 - 4x + 3?
Solution:
The vertex can be found using the formula x = -b/(2a). Here, a = 1, b = -4. Thus, x = 2. Plugging x back into the equation gives y = 1. So, the vertex is (2, 1).
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Q10. Solve for x: 2x^2 - 8 = 0.
Solution:
First, add 8 to both sides: 2x^2 = 8. Then divide by 2: x^2 = 4. Taking the square root gives x = ±2.
