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Question

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

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Solution

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


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