Ran out of paper space so I will type the rest here.

(x - 1) (2x + 3) (x + 2) = 0

x = 1
y = 2 (1)^3 + 3 (1)^2 - 4
y = 1

so (1, 1) is one point of intersection

x = -1.5
y = 2 (-1.5)^3 + 3 (-1.5)^2 - 4
y = -4

so (-1.5, -4) is another point of intersection

x = -2
y = 2 (-2)^3 + 3 (-2)^2 - 4
y = -8

so (-2, -8) is yet another point of intersection.

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Now, in (a), we need to show that b2 - 4ac >= 0 since they intersect (if they never ever intersect, then there will never be solutions or roots, so b2 - 4ac < 0).

In (b), we need to obtain the value of m and then solve a pair of simultaneous equations in two variables x and y which eventually transforms into a cubic equation.

I assume that you are able to solve a cubic equation on your own so I won't go into the details here.