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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 5/5

Find all real solutions of x3−1=0x^3 - 1 = 0.

  • A

    x=1x = 1 only

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  • B

    x=1,−1x = 1, -1

  • C

    x=1,0,−1x = 1, 0, -1

  • D

    x=−1x = -1 only

Explanation

x3−1=(x−1)(x2+x+1)x^3 - 1 = (x-1)(x^2 + x + 1). The quadratic x2+x+1x^2 + x + 1 has discriminant 1−4=−3<01 - 4 = -3 < 0, so no real roots. Only real solution: x=1x = 1.

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