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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 4/5

A polynomial of degree 4 has zeros at x=1,2,3x = 1, 2, 3. If the polynomial is monic and has zero x=1x = 1 of multiplicity 2, what is f(0)f(0)?

  • A

    66

    check_circle
  • B

    −6-6

  • C

    1212

  • D

    00

Explanation

f(x)=(x−1)2(x−2)(x−3)f(x) = (x-1)^2 (x-2)(x-3). Then f(0)=1⋅(−2)(−3)=6f(0) = 1 \cdot (-2)(-3) = 6.

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