Question

If one zero of the quadratic polynomial (k²+ k) x² + 68x + 6k is reciprocal of the other, find k.

Answer 1

Let the one zero be α and other zero be 1/α of p(x)
Let p(x) =( k²+ k) x²  +  68x  +  6k

On comparing with ax² + bx + c
a= k²+k , b= 68 , c= 6k

Product of zeroes(α.1/α)= c/a
α.1/α = 6k / k²+ k
1 = 6k / k² +k
k² + k = 6k
k² -6k + k =0
k² - 5k=0
k ( k - 5)= 0
k≠0
k-5= 0
k = 5

Hence, the value of k is 5.

HOPE THIS WILL HELP YOU...

Answer 2

Hope it helps .........☺