Question

The equation whose roots or solutions are 11 and -2 is:

a) x2 + 9x + 22 = 0
b) x2 + 7x + 2 = 0
c) x2 - 9x - 22 = 0
d) x2 - 7x - 2 = 0

Answer 1

9514 1404 393

Answer:

c) x^2 - 9x - 22 = 0

Explanation:

Consider the generic case ...

(x -a)(x -b) = 0 . . . . . . . has solutions x=a, x=b

Multiplying this out gives ...

x^2 -ax -bx +ab = 0

x^2 -(a+b)x +ab = 0

This tells you ...

• the coefficient of x is the opposite of the sum of the roots
• the constant is the product of the roots

The sum of roots is 11 +(-2) = 9, and the opposite of that is -9. You are looking for an equation with the term -9x. (Choice C matches)

The product of roots is (11)(-2) = -22. You are looking for an equation with a constant of -22. (Choice C matches that, too.)

The equation is ...

x^2 -9x -22 = 0