AMC 10 Step by Step
Log inSign up
Printable

2017 AMC 10A Problem 24

Include the solutionBack to the problem
2017 AMC 10A Problem 24AMC 10 Step by Step
Name:                             Date: September 13, 2026
Polynomials · difficulty 4 of 5 · about 6 min · position P21-25

For certain real numbers aa , bb , and cc , the polynomial g(x)=x3+ax2+x+10g(x) = x^3 + ax^2 + x + 10 has three distinct roots, and each root of g(x)g(x) is also a root of the polynomial f(x)=x4+x3+bx2+100x+c.f(x) = x^4 + x^3 + bx^2 + 100x + c. What is f(1)f(1) ?

  1. A)

    −9009-9009

  2. B)

    −8008-8008

  3. C)

    −7007-7007

  4. D)

    −6006-6006

  5. E)

    −5005-5005

Working