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.
By BYJU'S Exam Prep
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.
Related Questions:
- Find the Zeros of the Following Quadratic Polynomials x²+7x+10 and Verify the Relationship between the Zeros and the Coefficients
- If the sum of Zeros of the Quadratic Polynomial p(x) = kx²+2x+3k is Equal to their Product Find the Value of k
- If α and β are the Zeros of the Polynomial f(x)=x^2+x−2, Find the Value of (1/α−1/β)
- For the Following, Find a Quadratic Polynomial whose Sum and Product Respectively of the Zeros are as Given. Also Find the Zeroes of the Polynomial by Factorization: 21/8, 5/16
- Find the Zeroes of Quadratic Polynomial and Verify the Relationship Between the Zeroes and its Coefficient: T2-15
- Find the Zeros of the Following Quadratic Polynomials x2-2x-8 And Verify the Relationship Between the Zeros and the Coefficients
- P(x)=x2 + 2(√2)x – 6 Find the Zero of the Polynomial and Verify between Zero and Coefficients
- If α and β are the Zeros of the Quadratic Polynomial p(x) = 4x^2 − 5x − 1, Find the Value of α^2β + αβ^2
