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 the two zeroes of the f(t) = kt² + 2t + 3k be α and β

Sum of the zeroes (α + β)

Product of the zeroes αβ

`(-2)/k=(3k)/k`

`-2k = 3k^2`

`2k + 3k^2 = 0`

`k(3k + 2) = 0`

`k = 0`

`k=(-2)/3`