Question

graph the function in desmos: f(x) = -x⁴ + 3x³ - 2x what is the sum of your zeros? type your answer in the boxes

Explanation:

Step1: Factor the function

$f(x) = -x(x^3 - 3x^2 + 2) = -x(x - 1)(x^2 - 2x - 2)$? No, correct factoring: $f(x) = -x(x^3 - 3x^2 + 2) = -x(x - 1)(x^2 - 2x - 2)$ is wrong. Correct: $f(x) = -x(x^3 - 3x^2 + 2) = -x(x - 1)(x^2 - 2x - 2)$ no, better use Vieta's formula for quartic $ax^4 + bx^3 + cx^2 + dx + e$: sum of roots is $-b/a$.

Step2: Apply Vieta's formula

For $f(x) = -x^4 + 3x^3 + 0x^2 - 2x + 0$, $a=-1$, $b=3$. Sum of zeros = $-b/a = -3/(-1) = 3$.

Answer:

3