Nonlinear Functions

SAT Math· difficulty 5/5

A degree-4 polynomial has zeros at x=0x = 0 (multiplicity 1), x=1x = -1 (multiplicity 1), and x=2x = 2 (multiplicity 2). The polynomial is monic. What is f(1)f(1)?

  • A

    4-4

  • B

    2-2

    check_circle
  • C

    00

  • D

    22

Explanation

f(x)=x(x+1)(x2)2f(x) = x(x+1)(x-2)^2. f(1)=12(1)2=2f(1) = 1 \cdot 2 \cdot (-1)^2 = 2. Hmm, that gives 22. So correct should be 22. Recheck: f(1)=121=2f(1) = 1 \cdot 2 \cdot 1 = 2. So index 1 should be correct. Let me make answer index 1.

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