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Question

If α and β are the zeroes of a polynomial such that α+β=6 and αβ=4 then write the quadratic polynomial.

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Solution

Given that,
α+β=6 And αβ=4

The quadratic polynomial whose zeroes are α,β is,

f(x)=k[x2(α+β)x+αβ]

=k[x26x+4]

Where k is any non zero real number

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