Stuck with a polynomial question

The graph "kisses" the x axis at  x = 1   and goes through the x axis at x = -2

Therefore....we have that

y  =  (x + 2) (x - 1)^2

When x = 0, then "c"  =  2

So....we have that

( x + 2)(x-1)^2  = 2

(x + 2) ( x^2 - 2x + 1)  = 2

x^3 +2x^2 -2x^2 -4x + x+ 2  = 2

x^3 - 3x = 0

x( x^2 - 3) = 0       set both factors to 0 and solve for x

x = 0        and     x^2 - 3  = 0  ⇒  x^2 = 3 ⇒     x  = ± √3

Here's a graph :  https://www.desmos.com/calculator/co5bdggyfq

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