If α, β be the zeros of the polynomial 2x2 + 5x + k such that α2 + β2 + αβ = 21/4 then k =?

By Ritesh|Updated : November 6th, 2022
  1. 3
  2. -3
  3. -2
  4. 2

In the polynomials 2x2 + 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 2x2 + 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

Polynomial Operations

There are four main polynomial operations.

  1. Polynomial Addition - To add polynomials, always add the same term. Terms with the same variables and power. Adding polynomials always results in a polynomial of the same degree.
  2. Polynomial Subtraction - Polynomial subtraction is similar to addition, the only difference is the type of operation. So we subtract the same terms to get the solution.
  3. Polynomial Multiplication - Multiplying two or more polynomials always yields a higher degree polynomial (unless one of them is a constant polynomial).
  4. Division of Polynomials - The division of two polynomials may or may not result in polynomials.

Summary:

If α, β be the zeros of the polynomial 2x2 + 5x + k such that α2 + β2 + αβ = 21/4 then k =? (A) 3 (B) -3 (C) -2 (D) 2

If α, β be the zeros of the polynomial 2x2 + 5x + k such that α2 + β2 + αβ = 21/4 then k = 2. Polynomial is made up of two terms, where Poly (means “many”) and Nominal (means “terms.”). The polynomial 2x2 + 5x + k indicates the addition operation.

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