Question

on the graph of the equation y = 4x^3 - x^2 + 20x - 5, where would the function cross the x - axis? write your answer in fraction form, if applicable. (1 point)

Explanation:

Step1: Set y = 0

Set the function $y = 4x^{3}-x^{2}+20x - 5$ equal to 0, so $4x^{3}-x^{2}+20x - 5=0$.

Step2: Group terms

Group the terms as $(4x^{3}+20x)-(x^{2}+5)=0$.

Step3: Factor out common factors

Factor out $4x$ from the first - group and 1 from the second - group: $4x(x^{2}+5)-(x^{2}+5)=0$.

Step4: Factor out $(x^{2}+5)$

We get $(x^{2}+5)(4x - 1)=0$.

Step5: Solve for x

Since $x^{2}+5>0$ for all real x (because $x^{2}\geq0$ for all real x, so $x^{2}+5\geq5$), we set $4x - 1 = 0$. Solving $4x-1=0$ gives $x=\frac{1}{4}$.

Answer:

$x=\frac{1}{4}$