3.56: Normal intersecting a cubic again; definite integral

0606/22/O/N/23 — Question 5 · 10 marks

(a)
Find the equation of the normal to y=7x312x2+5x1y = 7x^{3} - 12x^{2} + 5x - 1 at (1, 1)(1,\ 1).
[5]
(b)
Find the xx-coordinates of the two points where the normal cuts the curve again, in the form x=a±bx = a \pm b.
[5]