Question

if alpha and beta are the zeros of polynomial PX = 4 x 2 - 5 x - 1 find value of Alpha 2 beta + alpha beta 2

Answer 1

Take alpha beta common Now ,we have to nd Alpha.beta(alpha+beta) Product of roots ×sum of roots =- b/a × c/a =5/4 × -1/4 =-5/16

Answer 2

Heya friend,
Here is it:

p(x) = $4x^{2}$ - 5x - 1
So, a = 4, b = -5, c = -1

Now,

α + β = -b/a
         = -(-5)/4
         = 5/4
and,
$α^{2}$β  = c/a
      = -1/4

As it is given,
⇒ $\alpha ^{2}$$\beta$ + $\beta ^{2}$α
⇒ αβ (α + β)
⇒ -1/4 × 5/4
⇒ -5/16


Thank you!!!
Manav