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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 5/5

The polynomial p(x)=x3−4x2+9x−10p(x) = x^3 - 4x^2 + 9x - 10 has a real root x=2x = 2. The other two roots are:

  • A

    1±2i1 \pm 2i

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  • B

    −1±2i-1 \pm 2i

  • C

    2±i2 \pm i

  • D

    1±i1 \pm i

Explanation

Divide by x−2x - 2: quotient x2−2x+5x^2 - 2x + 5. Solve: x=2±4−202=1±2ix = \dfrac{2 \pm \sqrt{4 - 20}}{2} = 1 \pm 2i.

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