SOLUTION: prove that the equation mx(x^2+2x+3)=x^2-2x-3 has exactly one real root if m=1 and exactly 3 real roots if m=-2/3

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Question 977117: prove that the equation mx(x^2+2x+3)=x^2-2x-3 has exactly one real root if m=1 and exactly 3 real roots if m=-2/3
Answer by anand429(138)   (Show Source): You can put this solution on YOUR website!
Simplifying, our equation becomes,

For m =1,
we get,

Comparing with standard form,

Let
=>
=>
Let
=>
=>
Now, let
=>
Clearly, h>0
hence, there is only one real root.
Similarly, put m = -2/3 and solve as above,
If h<0, it means all three roots are real.
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