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Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes, respectively. 4, 1

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

 4, 1

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5964 Points
11 months ago
Dear Student

Given,
Sum of zeroes, α + β = 4
Product of zeroes, αβ = 1

Therefore, if α and β are zeroes of any quadratic polynomial, then the polynomial can be written as:-

x^2– (α + β)x + αβ

x^2– 4x + 1

Thus, x^2– 4x +1 is the quadratic polynomial.

Thanks

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