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=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
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ProtonsTalk.
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ProtonsTalk.