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?

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shilpav
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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

    • This reply was modified 2 years, 10 months ago by ProtonsTalk.
    • This reply was modified 2 years, 8 months ago by ProtonsTalk.
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