If one zero of the quadratic polynomial, f(x) = 4×2 – 8kx – 9 is negative of the other, then the value of k is

By BYJU'S Exam Prep

Updated on: September 25th, 2023

If one zero of the quadratic polynomial, f(x) = 4×2 – 8kx – 9 is negative of the other, then the value of k is 0. When a variable term in the polynomial expression has the highest power of 2, the polynomial is said to be quadratic. Only the variable’s exponent is considered when determining a polynomial’s degree. It is not taken into account how strong a coefficient or constant term is. A quadratic equation or function is created when a quadratic polynomial equals 0. The roots or zeros of the quadratic equation are the names given to the solutions of such an equation.

Table of content

1. f(x) = 4×2 – 8kx – 9. Find the value of k if one zero of the quadratic polynomial is negative.
2. If one zero of the quadratic polynomial, f(x) = 4×2 – 8kx – 9 is negative of the other, then the value of k is

f(x) = 4×2 – 8kx – 9. Find the value of k if one zero of the quadratic polynomial is negative.

The question states If one zero of the quadratic polynomial, f(x) = 4×2 – 8kx – 9 is negative of the other, then the value of k is. The zeros or roots of the equation can be used to create a quadratic polynomial. Let’s say the two roots are -4 and 2. First, determine the total of the two roots. Sum of roots = -4 + 2 = -2. Then find the result of the two roots in step two. Product of roots = -4 * 2 = -8.

Replace these values in the formula x2 – (sum of the roots)x + (product of the roots). Thus, the quadratic polynomial is x2 + 2x – 8. The following are the steps to find the value of k of f(x) = 4×2 – 8kx – 9 quadratic polynomial:

Given: f(x) = 4×2 – 8kx – 9

Let the zeroes be α and -α

We know that:

Some of the zeroes = -b/a

Substituting the values we get:

α + (-α) = -(-8k)/4

0 = 8k/4

In simplification, we get the:

2k = 0

k = 0

Summary: