Nonlinear Functions

SAT Math· difficulty 5/5

A polynomial f(x)=a(xr1)m1(xr2)m2f(x) = a(x - r_1)^{m_1}(x - r_2)^{m_2} \cdots has degree 7, leading coefficient 2-2, and 3 distinct real zeros at 1,2,5-1, 2, 5. If the multiplicity of x=2x = 2 is 3 and x=1x = -1 is 2, what is the multiplicity of x=5x = 5?

  • A

    11

  • B

    33

  • C

    44

  • D

    22

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Explanation

Multiplicities sum to degree: 2+3+m=7m=22 + 3 + m = 7 \Rightarrow m = 2.

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