Question

if one zero of the polynomial f(x)=(k2+4)x2+13x+4k is the reciprocal of the other,then find thevalue of k .

Answer 1

Let one zero be a and other will be 1/a
By using product of zeros formula we get
a×1/a=4k/k²+4. {alpha×beta=c/a}
1=4k/k²+4
k²+4=4k
4k-4=k²
4(k-1)=k²
k-1=k²/4
k-1=+or-k/2
k-1=1/2
k=1/2+1=3/2{if k= +1/2}
k-1=-1/2
k=-1/2+1=1/2{if k= -1/2}
Therefore value of kis 3/2 or 1/2.
HOPE IT WAS HELPFUL