SOLUTION: If alpha and beta are the zeroes of the polynomial p(x)=9x^2-22x+8 then find the value of alpha ^4+beta ^4

Question 973113: If alpha and beta are the zeroes of the polynomial p(x)=9x^2-22x+8 then find the value of alpha ^4+beta ^4
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
9x^2-22x+8=0 Multiply the 8 by the leading coefficient, and rewrite leading coefficient as 1.
x^2-22x+72=0; factor into (x-18)(x-4)=0 divide now by the 9 you multiplied by, reducing all fractions.
(x-(18/9)) (x-(4/9))=0
(x-2) (9x-4)=0 are factors. They multiply out to the original polynomial.
The quadratic formula also works
(1/18) [22 +/- sqrt (484- 288)]= (1/18) [22 +/- sqrt (196)]
(1/18) (22+14) ; (1/18) (22-14)
roots are 2 and 4/9, same as above.
will take smaller zero to be alpha (4/9)
(4/9)^4= (256/6561)
2^4=16
16.0390

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