4
advanced-math

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

A

x2−6x+9=0x^2 - 6x + 9 = 0

B

x2+6x+9=0x^2 + 6x + 9 = 0

C

x2−9x+6=0x^2 - 9x + 6 = 0

D

x2+9x+6=0x^2 + 9x + 6 = 0

Correct Answer: A

Choice A is the correct answer. A quadratic equation can be written as x2−(Sum)x+(Product)=0x^2 - (Sum)x + (Product) = 0.

  1. Sum = 6 ⇒\Rightarrow coefficient of x is -6.
  2. Product = 9 ⇒\Rightarrow constant term is 9.
  3. Equation: x2−6x+9=0x^2 - 6x + 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.

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Set 12: Quadratic Equations and Functions 12