Question

If alpha and beta are the zeroes of 2x^2 + 3x - 5, find the value of alpha^2×Beta^3 + alpha^3×beta^2

Answer 1

Step-by-step explanation:

• Splitting method

2x^2+3x-5

sum=3;pro=-10

ie

the two values are 5 & -2

=> 2x^2+5x -2x-5=0

x(2x+5)-1(2x+5)=0

(x-1)(2x+5)=0

=> x=1 .....alpha

& x=-5/2.....beta

as we have learned:

alpha+beta=-b/a

alpha. beta=c/a

-b/a=-3/2

c/a=-5/2

alpha+beta=1+(-5/2)=-3/2..........(1)

alpha.beta=1×(-5/2)=-5/2...........(2)

as per the condition :

alpha^2×beta^3+alpha^3×beta^2

=> alpha^2 beta^2(beta +alpha)

apply (2)&(1)

(-5/2)^2(-3/2)

25/4×(-3/2)=

-75/8

I HOPE IT HELPS