Question

if one of the zeros of the quadratic polynomial f(x) = 4 x² - 8kx-9 is equal in magnitude but opposite in sign of the other, then find the value of k

Answer 1

◆ Quadratic Resolutions ◆

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Answer 2

Answer:

The value of k is 0

Step-by-step explanation:

Given that one of the zeros of the quadratic polynomial $f(x) = 4x^2-8kx-9$ is equal in magnitude but opposite in sign of the other, wehave to find the value of k

Let α and β be the zeros of the polynomial $4x^2-8kx-9$

It is given that α=-β

Then, α+β=0

i.e the sum of roots is 0

Compare equation  $f(x) = 4x^2-8kx-9$ with standard quadratic equation $ax^2+bx+c=0$, we get

a=4, b=8k, c=-9

$\text{Sum of roots =}\frac{-b}{a}=0$

$\frac{8k}{4}=0$

$2k=0$

$k=0$