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In the curve y=x^(3)+ax and y=bx^(2)+c p...

In the curve `y=x^(3)+ax and y=bx^(2)+c` pass through the point `(-1,0)` and have a common tangent line at this point then the value of `a+b+c` is

A

0

B

1

C

`-3`

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x)=x^(3)+ax and and g(x)=bx^(2)+x` pass through the point (`-1,0)`
`rArr" "f(-1)=0,g(-1)=0,`
`rArr" "-1-a=0 and b+c=0`
Also curves have common tangent at this point
`rArr" "f'(-1)=g'(-1)`
`rArr" "a+3=-2b`
From (i) and (ii)
`a=-1,b=-1,c=1,`
`rArr" hence "a+b+c=-1`
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