Answer: The graph of y=mx²-5x-2 has no x-intercepts for m<-25/8

Solution:
y=mx²-5x-2

To get x-intercepts, y must be zero:
=> y=0
=> mx²-5x-2=0

We can solve this equation using the quadratic formula:
ax²+bx+c=0; a=m, b=-5, c=-2

=> x = [-b ± sqrt( b² – 4ac) ] / (2a)
=> x = [-(-5) ± sqrt( (-5)² – 4(m)(-2) )] / (2(m))
=> x = [5 ± sqrt(25 + 8m)] / (2m)

This equation doesn’t have a solution (no x-intercepts) if:
25 + 8m < 0
=> 8m < -25
=> m < -25/8

Hence, The graph of y=mx²-5x-2 has no x-intercepts for m < -25/8

• This reply was modified 2 years, 11 months ago by ProtonsTalk.
• This reply was modified 2 years, 9 months ago by ProtonsTalk.