Question

if alpha and beta are the zeros of quadratic polynomial p(x)=4x2-5x-1,find the value of alpha square beta+ alpha beta square

Answer 1

Hey!

Given polynomial :- 4x²-5x-1

and alpha beta are it's zeros !

• Sum of Zeros =
$= \frac{ - coefficient \: of \: x}{coefficient \: of \: {x}^{2} }$

$\alpha + \beta = \frac{5}{4}$

• Product of Zeros =
$\frac{constant \: term}{coeff. \: \: of \: {x}^{2} }$

$\alpha \beta = \frac{ - 1}{4}$

# To find

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

$\alpha \beta ( \alpha + \beta )$

$\frac{ - 1}{4} \times \frac{5}{4} = \frac{ - 5}{16}$

Hence , value is -5/16

Answer 2

The answer is -5/16 ...
and the steps in the picture