Question

if alpha and beta are the zeros of the polynomial p x is equal to x square - 5 x + 6, then find the value of Alpha is to the power 4 into beta is to the power 3 + Alpha raised to the power 3 into beta raise to the power 4

Answer 1

p(x)=x square -5x+6 
x square -3x-2x+6
x(x-3)-2(x-3)
(x-3)(x-2)
i.e., alpha=3
       beta=2
two zeros of a polynomial.
The value of
alpha^4*beta^3+alpha^3*beta^4
3 to the power 4 * 2 to the power 3 + 3 to the power 3 * 2 to the power 4
81*8+27*16
648+432=1080

Answer 2

let alpha = a
beta = b

so
a and b are roots of.
x²-5x+6 = 0
=> (x-2)(x-3) = 0

so
roots are
x=2 and x=3

so
a⁴b³+b⁴a³
= 2⁴3³ + 3⁴2³
= 16×27+81×8
= 1080