Question

Let alpha and beta be the roots of the quadratic equation x² - 4x - 6 = 0. Find 1/a² + 1/b²​

Answer 1

7/9

Explanation:

Using vieta's formulas, we know that a + b = 4 and ab = -6.

1/a^2 + 1/b^2 can be written as (a^2 + b^2)/a^2b^2.

(a^2 + b^2)/a^2b^2 can be written as (a+b)^2 - 2ab/(a^2)(b^2)

{4^2 - 2(-6)}/(-6)^2 = 28/36 = 7/9