Question

If
$\alpha$
and
$\beta$
are the zeroes of the polynomial p (x) =
$k {x}^{2} + 4x + 4$
such that
$\alpha ^{2} + { \beta }^{2} = 24$
find the value of k.​

Answer 1

α+β=-4/k

αβ=4/k

α^2+β^2=24

(α+β)^2-2αβ=24

16/k^2-8/k=24

16-8k=24k^2

24^2+8k-16=0

6k^2+2k-4=0

3k^2+k-2=0

3k^2+3k-2k-2=0

3k(k+1)-2(k+1)=0

k=2/3,-1