If the sum of the zeros of the quadratic polynomial $f (t) = K t^{2} + 2 t + 3 K$ is equal to their product, find the value of $K$ .

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Solution

$f (t) = K t^{2} + 2 t + 3 K$

Let roots be $α, β$

$α + β = - \frac{2}{K}$

$α β = \frac{3 K}{K}$

According to question, $α + β = α β$

$∴ - \frac{2}{K} = \frac{3 K}{K}$

$∴ K = - \frac{2}{3}$

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