Kindly show me how to present on this question, is really burden me down. Thanks

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# Question

# Answer

sushi88

Your hypothesis one can be assumed as this to prove that m < 2 11/16.

Assume that the intersection of the two functions has real roots.

this means D > 0

6x^{2} -3x + 2m -5 = 0

a = 6, b = -3 , c =2m-5

(-3)^{2} – 4(6)(2m-5) > 0

9 – 48m + 120 > 0

-48m > -129

48m < 129

m < 129/48

m < 2 11/16

Hence 6x^{2} + 5(m-1) = 3(x + m) has real root if m < 2 11/16.

I also found one x = 1/4 (the same as you) and further D = 0 for the resulting quadratic, suggesting that the line is tangent at that one point on the curve. So I am not able to find 2 roots as stated in your second hypothesis.

s277400

Actually the question stated only the equations are real, it never indicates the equation has 2 point, so i think you explain is logical to me, thanks.

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