Question

Which of the following equations have complex roots?

A. x^2=−7x−2
B. x^2+3x+9=0
C. x^2=5x−1
D. x^2=−7x+2

Answer 1

B

Explanation:

A:

Completing the square: (x+ 7/2)^2 = -2 + 49/4 = 41/4, in the next step you'll be square rooting a positive number so it'll have real roots.

B:

Completing the square: (x+3/2)^2 = -9 + 9/4 = -27/4, you'll next be square rooting a negative number, so it'll have complex roots

C:

Completing the square: (x-5/2)^2 = -1 + 25/4 = 21/4, next you'll square root a positive number, so real roots

D:

Completing the square: (x+7/2)^2 = 2 + 49/4 = 57/4, square root a positive number, so real roots.