Question

if α and β are the zeroes of the quadratic polynomial p(x)=ax2+bx+c then evaluate 1/α^4 + 1/β^4

Answer 1

Answer:

p(x)=ax2+bx+c

α+β=-b/a

αβ=c/a

1/α+1/β-2αβ=(β+α)/αβ -2αβ

=(-b/a)/(c/a) -2c/a

=-b/c -2c/a

=-(ab+2c^2)/ca

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