Question

if alpha and beta are the zeros of the quadratic polynomial p of x
$= 4x { }^{2} -5x - 1$
find the value of
$\alpha {}^{2} \beta + \alpha \beta {}^{2}$
​

Answer 1

$<h1>SOLUTIONS:</h1>$

Given:p(x)=

$4x ^{2} + - 5x - 1$

To find the value of

$\alpha ^{2} \beta + \alpha \beta ^{2}$

First find the sum of Zeroes and product.

Sum of Zeroes is =-(coefficient of x)/(coefficient of x^2)

$\alpha + \beta = - ( - 5) \div 4$

$\alpha + \beta = 5 \div 4$

Their products will be

=constant/coefficient of x^2

=

$\alpha \beta = - 1 \div 4$

Now

$\alpha ^{2} \beta + \alpha \beta = \alpha \beta ( \alpha + \beta )$

so, put the value of products and sum now.

Putting we got=-1/4(5/4)

=-5/16

So, the value is -5/16