Answer:
[tex]x=2,x=\frac{30}{7},x=7[/tex]
Step-by-step explanation:
The given polynomial function is [tex]f(x)=7x^3-93x^2+368x-420[/tex].
Using the intercept method, we graph the given polynomial function.
The x-intercepts of the graph represents the zeros of the given function.
From the attached graph, the function has zeros at:
[tex]x=2,x=\frac{30}{7},x=7[/tex]
Answer:[tex]x=2,7,\frac{30}{7}[/tex]
Step-by-step explanation:
Given
[tex]7x^3-93x^2+368x-420=0[/tex]
Split the terms
[tex]7x^3-14x^2-79x^2+158x+210x-420=0[/tex]
[tex]7x^2\left ( x-2\right )-79x\left ( x-2\right )+210\left ( x-2\right )=0[/tex]
[tex]\left ( x-2\right )\left ( 7x^2-79x+210\right )=0[/tex]
[tex]\left ( x-2\right )\left ( 7x^2-49x-30x+210\right )=0[/tex]
[tex]\left ( x-2\right )\left ( 7x\left ( x-7\right )-30\left ( x-7\right )\right )=0[/tex]
[tex]\left ( x-2\right )\left ( x-7\right )\left ( 7x-30\right )=0[/tex]
therefore
[tex]x=2,7,\frac{30}{7}[/tex]
