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Question
If the sum of the zeros of the quadratic polynomial f(t) = kt2 + 2t + 3k is equal to their product, find the value of k.
Solution
Let the two zeroes of the f(t) = kt2 + 2t + 3k 𝑏𝑒 α and β
Sum of the zeroes (α + β)
Product of the zeroes αβ
`-2/k=(3k)/k`
`−2k = 3k^2`
`2k + 3k^2 = 0`
`k(3k + 2) = 0`
`k = 0`
`k=(-2)/3`
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