Question

Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function.

f(x) = -2x⁴ + 4x³ + 3x² + 18

Answer 1

If the rational number $\frac{a}{b},$ where $a\in\Z$ and $b\in\N,$ is a rational zero of the polinomial $f(x) = -2x^4 + 4x^3 + 3x^2 + 18,$ then according to the Rational Zeros Theorem $a$ is a divisor of 18 and $b$ is a divisor of $-2.$ Then all possible zeros are the following:

$1,\ -1,\ 2,\ -2,\ 3,\ -3,\ 6,\ -6,\ 9,\ -9,\ 18,\ -18,\ \frac{1}2,\ -\frac{1}2,\ \frac{3}2,\ -\frac{3}2,\ \frac{9}2,\ -\frac{9}2.$