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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 4/5

For what values of kk does kx2+4x+1=0kx^2 + 4x + 1 = 0 have no real solutions?

  • A

    0<k<40 < k < 4

  • B

    k>4k > 4 or k<0k < 0

  • C

    k<4k < 4

  • D

    k>4k > 4

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Explanation

Need b2−4ac<0b^2 - 4ac < 0: 16−4k<016 - 4k < 0, so k>4k > 4. (Also requires k≠0k \ne 0.)

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