If x^{2}-5x+4 is a factor of x^{4}-px^{2}+q, then what are the values of p and q respectively?

Explanation

Roots of x^2-5x+4=0 are x=1 and x=4. Both must be roots of x^4-px^2+q=0. Substituting x=1 yields 1-p+q=0 \implies p-q=1. Substituting x=4 yields 256-16p+q=0 \implies 16p-q=256. Subtracting the equations gives 15p=255 \implies p=17. Then q=16.

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