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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 4/5

The roots of x3−6x2+11x−6=0x^3 - 6x^2 + 11x - 6 = 0 are:

  • A

    x=−1,−2,−3x = -1, -2, -3

  • B

    x=1,6,−1x = 1, 6, -1

  • C

    x=1,2,3x = 1, 2, 3

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  • D

    x=1,2,6x = 1, 2, 6

Explanation

Test x=1x = 1: 1−6+11−6=01 - 6 + 11 - 6 = 0 ✓. Divide by x−1x - 1: quotient x2−5x+6=(x−2)(x−3)x^2 - 5x + 6 = (x-2)(x-3). Roots: 1,2,31, 2, 3.

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