Question

if a and b are zeros of the quadratic polynomial p(x)=4x^2-5x-1
find value of alpha+beta+alphabeta and alpha^2beta+alphabeta^2​

Answer 1

Answer:

1 , - 5/  16

Step-by-step explanation:

From the properties of quadratic polynomials / equations :

In an equation( ax^2 + bx + c = 0 )  : Sum of roots is represented by - b / a and product of roots is represented by c / a.

Thus, here, if in 4x^2 - 5x - 1, α and β are the roots :

= > α + β = - ( - 5 ) / 4 = 5 / 4

= > αβ = - 1 / 4

Therefore,

= > ( α + β ) + αβ

= > ( 5 / 4 ) - 1 / 4

= > ( 5 - 1 ) / 4

= > 4 / 4

= > 1

And,

= > α^2 β + β^2 a

= > αβ( α + β )

= > ( - 1 / 4 )( 5 / 4 )

= > - 5 / 16

Answer 2

Step-by-step explanation:

Aloha !

[tex] This is Astro [\tex]

Given,

p(x)=4x²-5x-1

Sum of roots= -b/a =-5/4

Product of roots = c/a= -1/4

Now,

We need

\alpha + \ beta+ \alpha\beta

=-5/4+(-¼)

=5-1/4

=4/4

=1

And,

\alpha²\beta+\alpha\beta²

=\alpha\beta(\alpha+\beta)

=-¼×(-5/4)

=5/16

Thank you

@ Twilight Astro ✌️☺️♥️