If the curves y = `x^3` + ax and y = `bx^2` + c pass thorugh 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 |
 |
y = `x^2`+ax and y =`bx^2` + c pass through the point (–1, 0).
ƒ(–1) = 0; g(–1) = 0;
–1 –1 = 0 and b + c = 0 ............(i)
Also curves have common tangent at this point
ƒ'(–1) = g'(–1)
a + 3 = –2b ...........(ii)
From (i) and (ii), we get
a = –1, b = –1, c = 1;
Hence a + b+ c = –1