4GMAT - Online GMAT Preparation

Question

If m and n are the roots of the quadratic equation x^2 - (2 root 5)x - 2 = 0, the value of m^2 + n^2 is:
A. 22
B. 24
C. 32
D. 20
E. 18

Choice B is the correct Answer

m and n are roots of the equation.

We have to find the value of m^2 + n^2

m^2 + n^2 = (m + n)^2 - 2mn

(m + n), the sum of the roots of a quadratic equation of the form ax^2 + bx + c = 0 is (-b/a)

mn, the product of the roots of the equation = c/a

The sum of the roots of the equation x^2 - (2 root 5)x - 2 = 0 is (2 root 5).
Product of the roots of the equation = -2.

Hence, (m + n)^2 - 2mn = (2 root 5)^2 - 2(-2) = 20 + 4 = 24.