Question

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

Answer 1

Let the zeroes of the given equation be α and β

according to the question

α+β=αβ

we know that sum of roots=α+β=-2/k (-coefficient of t/coefficient of t2)

and product of roots=αβ=3k/k (constant term/coefficient of t2)

so

-2/k=3k/k

k=-2/3

Hope my answer is correct :)