  # If α and β are the zeros of a quadratic polynomial such that α + β = 24 and α − β = 8, find a quadratic polynomial have α and β as its zeros.

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Updated on: October 17th, 2023 If α and β are the zeros of a quadratic polynomial such that α + β = 24 and α − β = 8, the quadratic polynomial is x2 − 24x + 128. Candidates should formulate polynomial equations in standard form before attempting to solve them. Factor it, then set all of the variable factors to zero once they have all reached zero. The solutions to the original equations are the responses to the derived equations.

Table of content ## α + β = 24 and α − β = 8, Find a Quadratic Polynomial have α and β as its Zeros.

The question states If α and β are the zeros of a quadratic polynomial such that α + β = 24 and α − β = 8, find a quadratic polynomial have α and β as its zeros.”The value of a variable in a polynomial may occasionally be zero. These numbers are described by polynomial zero. Sometimes people refer to them as polynomial roots. To get the solutions to the given problems we usually determine the zeros of quadratic equations.

Given, α + β = 24 and α − β = 8

(α−β)2 = (α+β)2 − 4αβ = 8*8

242 − 4αβ = 64

4αβ = 576 − 64 = 512

Or, αβ = 128

x2 − (α+β)x + αβ = 0

Hence, the required quadratic polynomial is x2 − (α+β)x + αβ.

Summary:

## If α and β are the zeros of a quadratic polynomial such that α + β = 24 and α − β = 8, find a quadratic polynomial have α and β as its zeros.

The quadratic polynomial is x2 − 24x + 128, if α and β are the zeros of a quadratic polynomial such that α + β = 24 and α − β = 8. Division, subtraction, multiplication, and addition are polynomial operations. Any polynomial can be easily solved using fundamental algebraic ideas and factorization strategies. Setting the right-hand side of the polynomial equation equal to zero is the first step in solving it.

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