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Question

Find a quadratic polynomial, the sum of whose zeroes is 4 and one zero is 5.


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Solution

Put the sum and product values of two roots of the quadratic equation.

Let αand β be the roots of quadratic equation.

Given, α+β=4 and one of the zeroes is 5.

Let α=5. So,

5+β=4β=-1

Substitute these values in the root form of quadratic equation x2-α+βx+αβ=0.

x2-4x+5-1=0x2-4x-5=0

Hence, the quadratic equation is x2-4x-5=0.


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