Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and their coefficients:

$f(x)\ =\ x^2\ –\ 2x\ –\ 8$

Given:

$f(x) = x^2 – 2x – 8$

To find:

Here, we have to find the zeros of f(x). 

Solution:

To find the zeros of f(x), we have to put $f(x)=0$.

This implies,

$x^2 – 2x – 8 = 0$

$x^2 – 4x + 2x – 8 = 0$

$x(x – 4) + 2(x – 4) = 0$

$(x – 4)(x + 2) = 0$

$x-4=0$ and $x+2=0$

$x = 4$ and $x = -2$

Therefore, the zeros of the quadratic equation $f(x) = x^2 – 2x – 8$ are $4$ and $-2$.

Verification:

We know that, 

Sum of zeros $= -\frac{coefficient of x}{coefficient of x^2}$

                       $= –\frac{(-2)}{1}$

                       $=2$

Sum of the zeros of $f(x)=4+(-2)=4-2=2$ 

Product of roots $= \frac{constant}{coefficient of x^2}$

                            $= \frac{(-8)}{1}$

                            $= -8$

Product of the roots of $f(x)=4\times(-2) =-8$

Hence, the relationship between the zeros and their coefficients is verified.

Updated on: 10-Oct-2022

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