Quadratic Equations - Problem Set

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Q1. 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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Q2. 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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Q3. 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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Q4. 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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Q5. 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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Q6. Which of the following inequalities represents the solution to 3x + 2 > 11?

Solution:

Subtracting 2 from both sides gives 3x > 9. Dividing by 3 results in x > 3.

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Q7. 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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Q8. 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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Q9. Find the value of x in the equation 3x^2 + 12x + 12 = 0.

Solution:

Dividing the entire equation by 3 gives x^2 + 4x + 4 = 0. Factoring gives (x + 2)(x + 2) = 0, so x = -2.

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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.