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Question

Find a quadratic polynomial whose zeroes are -4 and -5.


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Solution

Find the sum and product of the roots of the quadratic equation.

Let αand β be the roots of the quadratic equation.

Sum of the zeroes

α+β=-4-5α+β=-9

Product of the zeroes

αβ=20

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

x2+9x+20=0

Hence, the quadratic equation is x2+9x+20=0.


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