Question

If alpha and beta are zeroes of a polynomial kx^2+6x+6. Find k such that alpha^2+beta^2=24

Answer 1

kx^2+6x+6

Let α and βbe roots of the above equation

⇒ Sum of roots = -x coefficient/x² coefficient i.e α+β=-6/k

product of roots = constant term/x² coefficient i.e αβ=6/k

α²+β² = (α+β)² - 2*αβ = (-6/k)²-2*(6/k)

                                  = (36-12k)/k²

So  (36-12k)/k² = 24

⇒24k²+12k-36=0

⇒2k²+k-3=0

⇒k=-3/2 or 1