Question

find the zeros of quadratic polynomial 2 x square - 9 - 3 x and verify the relationship between the zeros and the coefficient
answer me plz

Answer 1

hope this answer will help you.

Answer 2

The zeros of the quadratic polynomial are $\alpha =3,\ \beta=-\frac{3}{2}$.

Step-by-step explanation:

Given : The quadratic polynomial $2x^2-9-3x$

To find : The zeros of quadratic polynomial and verify the relationship between the zeros and the coefficient ?

Solution :

First we find the roots of the polynomial by middle term split,

$2x^2-3x-9=0$

$2x^2-6x+3x-9=0$

$2x(x-3)+3(x-3)=0$

$(x-3)(2x+3)=0$

$x=3,-\frac{3}{2}$

So, the roots are $\alpha =3,\ \beta=-\frac{3}{2}$

The sum and product of the roots of the equation $ax^2+bx+c=0$ is

$\alpha+\beta =-\frac{b}{a}$

$\alpha \beta=\frac{c}{a}$

Here, a=2, b=-3 and c=-9

To verify substitute the values,

The sum of the roots,

$3+(-\frac{3}{2}) =-\frac{-3}{2}$

$\frac{6-3}{2}=\frac{3}{2}$

$\frac{3}{2}=\frac{3}{2}$

True.

The product of the roots,

$3\times -\frac{3}{2}=\frac{-9}{2}$

$-\frac{9}{2}=-\frac{9}{2}$

True.