Take a look at y = mx^2 – 5x – 2. This is a quadratic equation with a=m, b= -5 and c= -2. What is the discriminant, b^2 - 4ac? (-5)^2 - 4(m)(-2).
There will be 2 complex roots if this discrim. is < 0. Thus, solve
25 + 8m < 0:
Subtr. 25 from both sides: 8m < -25
Div. both sides by 8: m < -25/8
Conclusion: If m is less than -25/8, there will be no real roots (and thus, no x-intercepts).
