Home › Forums › Math › For what values of m does the graph of y = mx^2 – 5x – 2 have no x-intercepts? › Reply To: For what values of m does the graph of y = mx^2 – 5x – 2 have no x-intercepts?

July 19, 2021 at 7:27 pm
#10318

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**Answer:** The graph of y=mx^{2}-5x-2 has no x-intercepts for m<-25/8

**Solution:
**y=mx

^{2}-5x-2

To get x-intercepts, y must be zero:

=> y=0

=> mx^{2}-5x-2=0

We can solve this equation using the quadratic formula:

ax^{2}+bx+c=0; a=m, b=-5, c=-2

=> x = [-b ± sqrt( b^{2 }– 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=mx^{2}-5x-2 has no x-intercepts for m < -25/8

- This reply was modified 2 years, 4 months ago by ProtonsTalk.
- This reply was modified 2 years, 1 month ago by ProtonsTalk.