Question

22. Which equation has solutions of -2 and 3?

A. y=x²+x-6
B. y=x²-x-6
C. y = x + 5x + 6
D. y = x2-5x+6

Answer 1

B. y=x²-x-6

Explanation:

Consider the product ...

0 = (x -a)(x -b) = x² -(a+b)x +ab

This equation has solutions x=a and x=b. You will note that ...

• the constant is the product of the solutions (ab)
• the coefficient of x is the opposite of their sum (-(a+b))

For solutions of -2 and 3, the constant will be (-2)(3) = -6. This eliminates choices C and D.

The sum of the solutions is -2+3 = 1, so the coefficient of x is -1, matching choice B.