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.A. ` a=(1)/(2),b=-(3)/(4), c=3 `B. ` a=-(1)/(2),b=-(3)/(4), c=3 `C. ` a=(1)/(2),b=(3)/(4), c=3 `D. none of these

The curve `y=a x^3+b x^2+c x+5`touches the x-axis at `P(-2,0)`and cuts

1.	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.A. ` a=(1)/(2),b=-(3)/(4), c=3 `B. ` a=-(1)/(2),b=-(3)/(4), c=3 `C. ` a=(1)/(2),b=(3)/(4), c=3 `D. none of these
Answer» Correct Answer - B We have, ` y=ax^(3)+bx^(2)+cx +5 " "...(i) ` ` rArr (dy)/(dx)=3ax^(2) + 2bx +c " "...(ii) ` Since the curve (i) touches x-axis at A(-2,0). Therefore, point A lies on (i) and `((dy)/(dx))_(A)=0.` ` therefore -8a+4b-2c+5=0 " "...(iii) ` and, ` 12a-4b+c=0 " "...(iv) ` The curve (i) cuts y-axis at B(0,5). It is given that ` ((dy)/(dx))_(B)=3 rArr c=3 ` Putting c = 3 in (iii) and (iv) and solving them, we get ` a=-(1)/(2) " and " b=-(3)/(4) `

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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.A. ` a=(1)/(2),b=-(3)/(4), c=3 `B. ` a=-(1)/(2),b=-(3)/(4), c=3 `C. ` a=(1)/(2),b=(3)/(4), c=3 `D. none of these

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