If the sum if the zeros of the polynomial kt^2 +2t +3k is equal to their product find the value of k

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Solution

Given quadratic polynomial f(t) = kt²+ 2t +3k

α,β are the roots of the quadratic polynomial then

α+β = -2/k and αβ = 3k/k

According to the condition α+β = αβ

-2/k = 3

∴ k = -2/3.

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