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Question

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
14,14

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Solution

If α and β are the zeroes of a quadratic polynmial, then the polynomial can be written as follows-
p(x)=x2(α+β)x+(αβ)
Whereas
α+β= Sum of roots
αβ= Product of roots
Now according to the question,
Sum of roots =α+β=14
Product of roots =αβ=14
Therefore the quadratic polynomial will be-
p(x)=x2(14)x+(14)
p(x)=x2+x4+14
Hence the quadratic polynomial will be x2+x4+14.

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