The curve y= ax3+ bx2+cx + 5 touches the x-axis at P(-2, 0) and cuts the y-axis at a point Q where its gradient is 3, then the value of -10 a- 100b+ 1000 c must be

∵dydx=3ax2+2bx+c----iSince, the curve y = ax3 + bx2 + cx +5 touches X-axis at P(-2 0) then X-axis is the tangent at (-2, 0) the curvemeets Y-axis in (0, 5).∴ dydx(0,5)=0+0+c=3 (given) ----ii and dydx(−2,0)=0⇒12a−4b+c=0⇒12a−4b+3=0  [from Eq. (ii)] ..........(iii)and (-2, 0) lies on the curve, then0=−8a+4b−2c+5⇒ −8a+4b−1=0⇒ 8a−4b+1=0----ivFrom Egs. (ii) and (iv) we geta=−12,b=−34∴−10a−100b+1000c=−10×−12−100×−34+1000×3=5+75+3000=3080