Question

If the sum of the zeros of the quadratic polynomial f(x)=kx2 +2x+3k is equal to their product find the value of k

Answer 1

Let f(x) = kx2 + 2x + 3k

Here a = k, b = 2 and c = 3k

Sum of zeroes, α + β = -b/a = -(2)/k = -2/k

Product of zeroes, αβ = c/a = 3k/k = 3

Given,

Sum of zeroes = Product of zeroes

-2/k = 3

k = -2/3

So, value of k = -2/3