Question

The curve y$=a{x}^3+b{x}^2+cx+5$ touches the x-axis at $P(-2,0)$ then $C=?$

• A. $4a+5$
• B. $4a-5$
• C. $5-4a$
• D. $0$

Answer 1

The correct option is A $4a+5$

As the curve pases through the point $(-2,0)$

So,

$0=-8a+4b-2c+5$

$8a-4b+2c=\mathrm{5.....}\left(i\right)$

Also, the tangent parallel to x-axis is 0. Hence,

$3a{x}^2+2bx+c=\frac{dy}{dx}$

$12a-4b+c=\mathrm{0.......}\left(ii\right)$

Subtracting (ii) from (i), we get

$-4a+c=5$

$c=4a+5$