Answer:
-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.
