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

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  • #10316
    hemanthk
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      Please add the solution.

      #10318
      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, 11 months ago by ProtonsTalk.
        • This reply was modified 2 years, 8 months ago by ProtonsTalk.
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