Question

if the sum of zero of a quadratic polynomial p(x)=kx^2+2x-3k is equal to twice 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.