1

Set 15: Quadratic Equations (Intermediate)

Explanation

Answer: B

Find the roots of the equation: (x3)(x+2)=0(x - 3)(x + 2) = 0

A.

x=3,2x = -3, 2

B.

x=3,2x = 3, -2

✓ Correct
C.

x=3,2x = 3, 2

D.

x=3,2x = -3, -2

Detailed Explanation

Choice B is correct. Choice B is the correct answer. The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero. 1. Set the first factor to zero: x3=0x=3x - 3 = 0 \Rightarrow x = 3. 2. Set the second factor to zero: x+2=0x=2x + 2 = 0 \Rightarrow x = -2. The roots are 3 and -2. Choice A is incorrect because the signs are flipped. This is a very common error. Choice C is incorrect because x+2=0x+2=0 implies x=2x=-2, not 2. Choice D is incorrect because x3=0x-3=0 implies x=3x=3, not -3.

Key Steps:

The correct answer is x=3,2x = 3, -2

Why others are wrong:
A: Choice A 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.

🎯 Keep Practicing!

Master all sections for your best SAT score