Quadratic Formula Applications

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Q1. What are the solutions to the equation x^2 - 10x + 21 = 0?

Solution:

Factoring gives (x - 3)(x - 7) = 0. Thus, the solutions are x = 3 and x = 7.

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Q2. Find the roots of the quadratic equation 3x^2 + 6x + 3 = 0.

Solution:

Dividing the equation by 3 gives x^2 + 2x + 1 = 0, which factors to (x + 1)(x + 1) = 0. Thus, x = -1.

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Q3. Solve for x in the equation x^2 + 4x + 4 = 0.

Solution:

This factors to (x + 2)(x + 2) = 0. Therefore, x = -2.

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Q4. What are the solutions to 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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Q5. What are the solutions to the equation x^2 - 4 = 0?

Solution:

Factoring gives (x - 2)(x + 2) = 0. Thus, the solutions are x = 2 and x = -2.

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Q6. If 2x + 3 > 7, what is the solution for x?

Solution:

Subtract 3 from both sides: 2x > 4. Divide by 2: x > 2.

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Q7. Find the roots of the quadratic equation 4x^2 - 12x + 9 = 0.

Solution:

This can be factored as (2x - 3)(2x - 3) = 0. Thus, x = 3.

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Q8. Solve for x: 4x^2 + 8x = 0.

Solution:

Factor out 4x: 4x(x + 2) = 0. Thus, x = 0 or x + 2 = 0 gives x = -2.

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Q9. Find the value of x in the inequality 3x - 5 < 4.

Solution:

Add 5 to both sides: 3x < 9. Divide by 3: x < 3.

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Q10. Solve the quadratic equation x^2 + 6x + 9 = 0.

Solution:

This can be factored as (x + 3)(x + 3) = 0. Therefore, x + 3 = 0 gives x = -3.