Answer:
B.) 1
Step-by-step explanation:
Roots will be rational if they adhere to the limits imposed by the Rational Root Theorem. That is, they must be of the form ...
±(divisor of the constant)/(divisor of the leading coefficient)
In this case, that means rational roots will be one of ±{1/2, 1, 2}.
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Graph
The graph is shown in the attachment. Only one of the roots is rational:
x = -1/2
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Factoring
You can also see what the roots are by factoring the equation. This one factors by pairs of terms.
f(x) = (2x³ +x²) -(4x +2) = x²(2x +1) -2(2x +1)
f(x) = (2x +1)(x² -2) = (2x +1)(x -√2)(x +√2) ⇒ x = -1/2, ±√2
This shows one rational root and two irrational roots.
