Answer
-1/2 and 1 of multiplicity one
See graph below.
Work Step by Step
The question asks for all real zeros of P(x), their respective multiplicities, and the graph of P(x)
Given $P(x) = 2x^4 + x^3 + 2x^2 - 3x - 2$
$P(x) = 2x^4 +x^3 + 2x^2 + x - 4x - 2$
$P(x) = x^3 (2x + 1) + x (2x + 1) -2 (2x + 1)$
$P(x) = (x^3 + x - 2) (2x + 1)$
$P(x) = (x-1)(x^2 + x + 2) (2x + 1)$
Set $P(x) = 0$
Thus x = -1/2, 1
To determine multiplicity, it is the power of the root determined from setting P(x) = 0
So -1/2 and 1 of multiplicity one
See graph below.
