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 $0$.
Related Articles
- If one of the zeroes of the quadratic polynomial $( k-1)x^{2}+kx+1$ is $-3$, then find the value of $k$.
- If 2 is a zero of the polynomial $p(x)= 4x^2+2x-5a$, then find the value of a.
- If sum of the squares of zeroes of the quadratic polynomial $6x^2+x+k$ is $\frac{25}{36}$, then find the value of $k$.
- If sum of the square of zeroes of the polynomial $f(x)=x^2−8x+k$ is $40$, find the value of $k$.
- If one of the zeroes of the polynomial $3x^2+8x+k$ is the reciprocal of the other, then what is the value of $k$?
- If $x = 3$ is one root of the quadratic equation $x^{2}-2kx-6=0$ , then find the value of $k$.
- If the sum of zeroes of the quadratic polynomial $3x^2–kx+6$ is $3$, then find the value of $k$.
- If the sum of the zeroes of the quadratic polynomial $f(t)\ =\ kt^2\ +\ 2t\ +\ 3k$ is equal to their product, then find the value of $k$.
- If the sum of the zeroes of the polynomial $P(x)=( k^{2}-14)x^{2}-2x-12$ is $1$. Then find the value of $k$.
- If the zeros of the polynomial $f(x)\ =\ x^3\ -\ 12x^2\ +\ 39x\ +\ k$ are in A.P., find the value of $k$.
- Find the value of k, if $x – 1$ is a factor of $4x^3 + 3x^2 – 4x + k$.
- If one root of $5x^{2}+13x+k=0$ is the reciprocal of the other root, then find the value of $k$.
- Find the zeroes of the quadratic polynomial $f( x)=x^2-3x-28$.
- If the squared difference of the zeros of the quadratic polynomial $f(x)\ =\ x^2\ +\ px\ +\ 45$ is equal to 144, find the value of $p$.
- If $x = 2$ is a root of the polynomial $f(x) = 2x^2-3x + 7a$, find the value of $a$.
Kickstart Your Career
Get certified by completing the course
Get Started