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

Given:

One of the zeros of the quadratic polynomial $f(x)\ =\ 4x^2\ –\ 8kx\ –\ 9$ is negative of the other. 

To do:

Here, we have to find the value of k. 

Solution:
 

Let the zeros of the polynomial be $α$ and $-α$.

We know that, 

Sum of the roots of the quadratic polynomial$=\frac{-(-8k) }{4}$

Therefore, 

$α+(-α)=\frac{-(-8k) }{4}$

$0=\frac{-(-8k) }{4}$

$8k=0$

$k=0$

The value of $k$ is $0$.

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Updated on: 10-Oct-2022

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