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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 5/5

The equation x2−2(k+1)x+(k2+3)=0x^2 - 2(k+1)x + (k^2 + 3) = 0 has two distinct real roots. What is the range of kk?

  • A

    k>1k > 1

    check_circle
  • B

    k>−1k > -1

  • C

    k≠1k \ne 1

  • D

    k<1k < 1

Explanation

D=4(k+1)2−4(k2+3)=4(2k−2)=8(k−1)>0D = 4(k+1)^2 - 4(k^2 + 3) = 4(2k - 2) = 8(k - 1) > 0, so k>1k > 1.

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