Question

if alfa and beta are zeroes of kx^2+lx+m then alfa^2+beta^2is​

Answer 1

Solution:

The given polynomial is

f(x) = kx² + lx + m

Since α and β are the zeroes of f(x), by the relation between zeroes and coefficients, we get

α + β = - l/k

αβ = m/k

Now, α² + β²

= (α + β)² - 2αβ

= (- l/k)² - 2 (m/k)

= l²/k² - 2m/k

= (l² - 2mk)/k²