Set 12: Quadratic Equations (Intermediate)

Explanation

Answer: A

If the sum of roots is 6 and the product is 9, what is the equation?

$x^2 - 6x + 9 = 0$

✓ Correct

$x^2 + 6x + 9 = 0$

$x^2 - 9x + 6 = 0$

$x^2 + 9x + 6 = 0$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. A quadratic equation can be written as $x^2 - (Sum)x + (Product) = 0$ . 1. Sum = 6 $\Rightarrow$ coefficient of x is -6. 2. Product = 9 $\Rightarrow$ constant term is 9. 3. Equation: $x^2 - 6 x + 9 = 0$ . Choice B is incorrect because the sign of the linear term is opposite the sum. Choice C is incorrect because it swaps sum and product. Choice D is incorrect because of both errors.

Key Steps:

•

The correct answer is $x^2 - 6x + 9 = 0$

Why others are wrong:

B: Choice B is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

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