-0.5x^4+ 3x^2 + 2x

Find the x intercepts

-2, -0.732, 0, 2.732.

Step-by-step explanation:

We need to solve for x:

-0.5x^4+ 3x^2 + 2x = 0  

x(-0.5x^3  + 3x + 2) = 0      So one x-intercepts is x = 0.

-0.5x^3  + 3x + 2 = 0

Possible roots are   2 or - 2:

f(-2) = -0.5(-2)^3 + 3(-2) + 2 =  4 - 6 + 2 = 0.

So x = -2 is a root and x+ 2 is a factor.

Dividing the expression by x + 2:

x + 2 ) -0.5x^3 + 0x^2 + 3x + 2( -0.5x^2 + x + 1  < Quotient.

          -0.5x^3 -   x^2

                            x^2 + 3x

                            x^2 + 2x

                                       x + 2

                                       x + 2

-0.5x^2 + x + 1 = 0

x = [ -1 +/-√(1 - 4*-0.5* 1) ] / -1

x =  (-1 +/- √3) / -1

x = -0.732, 2.732.