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The curve y=a x^3+b x^2+c x+5 touches th...

The curve `y=a x^3+b x^2+c x+5` touches the x-axis at `P(-2,0)` and cuts the y-axis at the point `Q` where its gradient is 3. Find the equation of the curve completely.

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The correct Answer is:
`a=-1/2, b=-3/4, c=34`
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