If α and 1/α are the zeroes of P(x) = 4×2 – 2x + (k – 4), Find k

By BYJU'S Exam Prep

Updated on: September 25th, 2023

If α and 1/α are the zeroes of P(x) = 4x²– 2x + (k – 4), the value of k is 8.

Let the given polynomial be p(x) = 4x²– 2x + (k – 4)

Given, α and 1/α are the zeroes of the given polynomial

We know that product of zeroes = c/a

α x 1/α = (k – 4)/4

1 = (k – 4)/4

k – 4 = 4

On simplification we get

k = 8

Table of content

1. If α and 1/α are the zeroes of P(x) = 4×2 – 2x + (k – 4), Find k

Polynomial

Polynomial is formed composed of the phrases Nominal, which means erms, and Poly, which means many. An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable). The expression is divided into three categories: monomial, binomial, and trinomial depending on how many terms are included in it.

Degree of a Polynomial

The highest exponent of a monomial contained within a polynomial is referred to as the polynomial’s degree. As a result, a polynomial equation with one variable having the biggest exponent is referred to as a polynomial degree.

Polynomial Equations

Expressions with many constants and variables are called polynomial equations. The greatest degree is written first and the constant term is written last in a polynomial equation using the standard form.

Summary:-