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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 5/5

A polynomial p(x)p(x) with integer coefficients has roots x=2x = 2 and x=1+ix = 1 + i. What is the minimum degree of p(x)p(x)?

  • A

    44

  • B

    22

  • C

    55

  • D

    33

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Explanation

Complex roots come in conjugate pairs for real-coefficient polynomials. So 1−i1 - i is also a root. Total roots: 2,1+i,1−i2, 1+i, 1-i, giving minimum degree 3.

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