Let f(x) and g(x) be two monic cubic polynomials, and let r be a real number. Two of the roots of f(x) are r+1 and r+7. Two of the roots of g(x) are r+3 and r+9, and f(x)−g(x)=r for all real numbers x. Find r.

Drew Williamson

Drew Williamson

Answered question


f(x) and g(x) are monic cubic polynomials, with f ( x ) g ( x ) = r. If f has roots r+1 and r+7, and g has roots r+3 and r+9, then find r

Answer & Explanation

Dakota Duarte

Dakota Duarte

Beginner2022-09-09Added 7 answers

Hint: We have f ( r + 3 ) = r and p = 9 8 r + 3 easily follows. Then, f ( r + 9 ) = r = 2 r + 96

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