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Question

If α and β are zeros of a quadratic polynomial such that α+β=24 and αβ=8 find a quadtratic polynomial having α and β as it's zeros.

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Solution

α+β=24

αβ=8

(αβ)2=(α+β)24αβ=82

or,2424αβ=64

or,4αβ=57664=512

or,αβ=128

x2(α+β)x+αβ=0

or,x224x+128=0

Hence x224x+128=0 is the quadratic polynomial for the required condition

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