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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 5/5

For what values of mm does x2+(m+1)x+(m+4)=0x^2 + (m+1)x + (m+4) = 0 have no real solutions?

  • A

    m<−5m < -5 or m>3m > 3

  • B

    −3<m<5-3 < m < 5

    check_circle
  • C

    −5<m<3-5 < m < 3

  • D

    m<−3m < -3 or m>5m > 5

Explanation

D=(m+1)2−4(m+4)=m2+2m+1−4m−16=m2−2m−15<0D = (m+1)^2 - 4(m+4) = m^2 + 2m + 1 - 4m - 16 = m^2 - 2m - 15 < 0. (m−5)(m+3)<0(m-5)(m+3) < 0: −3<m<5-3 < m < 5.

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