Question

If the sum of the zeros of the quadratic polynomial f(t) = kt² + 2t + 3k is equal to their product, find the value of k.

Answer 1

Let one root of the given quadratic polynomial is α

Other root of the given quadratic polynomial is β

Sum of the roots

Product of the roots

According to the question:

sum of zeros = product of zeros

\(-\frac{2}{k}\) = 3

k = \(-\frac{2}{3}\)

Answer 2

Sum of zeros= -b/a = -2/k

Product of zeros= c/a= 3k/k = 3

-2/k = 3  {Sum= Product}

k= -2/3