If one zero of the quadratic polynomial, f(x) = 4x2 - 8kx - 9 is negative of the other, then the value of k is.

By Ritesh|Updated : November 13th, 2022

(a) 0

(b) 1

(c) 2

(d) 3

The value of k is 0. Steps to find the value of k of f(x) = 4x2 - 8kx - 9 quadratic polynomial:

Given:

f(x) = 4x2 - 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

Hence, option a is correct.

Quadratic Polynomial

When a variable term in the polynomial expression has the highest power of 2, the polynomial is said to be quadratic. Only the exponent of the variable is taken into account when determining a polynomial's degree.

It is not taken into account how strong a coefficient or constant term is. A quadratic equation or quadratic function is created when a quadratic polynomial is equal to 0. The roots or zeros of the quadratic equation are the names given to the solutions of such an equation.

How can a quadratic polynomial be found?

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. The following are the steps to finding the quadratic polynomial:

First, determine the total of the two roots. Sum of roots = -4 + 2 = -2.

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

Summary:

If one zero of the quadratic polynomial, f(x) = 4x2 - 8kx - 9 is negative of the other, then the value of k is.

If one zero of the quadratic polynomial, f(x) = 4x2 - 8kx - 9 is negative of the other, then the value of k is 0. The polynomial function is denoted by f(x) where x represents the variable.

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