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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 4/5

The equation x2+(k−2)x+1=0x^2 + (k-2)x + 1 = 0 has exactly one solution. What is kk?

  • A

    k=4k = 4 only

  • B

    k=0k = 0 only

  • C

    k=±2k = \pm 2

  • D

    k=0k = 0 or k=4k = 4

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Explanation

Discriminant =0= 0: (k−2)2−4=0(k-2)^2 - 4 = 0, (k−2)2=4(k-2)^2 = 4, k−2=±2k - 2 = \pm 2, k=0k = 0 or 44.

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