If alpha and beta are the zeros of the polynomial p(x)=2×2+5x+k such that α2 + β2 + αβ = 21/4 then k =?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

If alpha and beta are the zeros of the polynomial p(x)=2×2+5x+k such that α2 + β2 + αβ = 21/4 then k is 2. A polynomial may have some values of the variable for which it will have a zero value. These numbers are referred to as polynomial zeros. They are also sometimes referred to as polynomial roots. To obtain the solutions to the given problem, we often determine the zeros of quadratic equations. We’ll guide you through the question’s step-by-step solution in this post.

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1. If α, β be the zeros of the polynomial 2×2+5x+k such that α 2 + β 2 + αβ= 21/4 then find k
2. If alpha and beta are the zeros of the polynomial p(x)=2×2+5x+k such that α2 + β2 + αβ = 21/4 then k =?

If α, β be the zeros of the polynomial 2×2+5x+k such that α 2 + β 2 + αβ= 21/4 then find k

The question states “If alpha and beta are the zeros of the polynomial p(x)=2×2+5x+k such that α2 + β2 + αβ = 21/4 then k=?” The points where a polynomial becomes zero overall are known as the zeros of the polynomial. The term “zero polynomial” refers to a polynomial with a value of zero (0). The highest power of the variable x is referred to as a polynomial’s degree. In the polynomials 2×2 + 5x + k, if α, β are the zeros, where α2 + β2 + αβ = 21/4 then the value of k is 2.

It is given that: α, β are zeros of the polynomial 2×2 + 5x + k

We know that:

α + β = -b/a

α.β = c/a

α + β = -5/2

α.β = k/2

(α + β)2 = (-5/2)2

α2 + β2 + 2αβ = 25/4

α2 + β2 + αβ + αβ = 25/4

21/4 + k/2 = 25/4

k/2 = 25/4 – 21/4

k/2 = 4/4

k/2 = 1

k = 2

Summary: