Question

Find the values of k if roots of equation(k^2+2)x^2+7x+3k=0are receprocal of each other

Answer 1

Let the root be a and 1/a

(k²+2)x²+7x+3k=0

Product of roots=c/a

a×1/a=3k/(k²+2)

1=3k/(k²+2)

k²+2=3k

k²-3k+2=0

k²-2k-k+2=0

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

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

(k-1)=0

k=1

(k-2)=0

k=2

the value of k can be 1 or 2

@Altaf