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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 5/5

The equation kx2−(k+1)x+1=0kx^2 - (k+1)x + 1 = 0 has two equal roots (k≠0k \ne 0). What is kk?

  • A

    k=2k = 2

  • B

    k=1k = 1

    check_circle
  • C

    k=−1k = -1

  • D

    k=1/2k = 1/2

Explanation

D=(k+1)2−4k=k2+2k+1−4k=(k−1)2=0D = (k+1)^2 - 4k = k^2 + 2k + 1 - 4k = (k-1)^2 = 0, so k=1k = 1.

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