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Question

If α and β are the zeros of the quadratic polynomial such that α+β=24 and αβ=8 find a quadratic polynomial having a α and β as its zeros.

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Solution

α+β=24(i)
αβ=8(ii)
Adding (i) and (ii)
2α=32
α=16
β=8
roots are 16 and 8
Sum=24
Product=128
f(x)=K(x224x+128)

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