Question 8
Find all zeros of the function $f(x)=8 x^{3}-42 x^{2}+67 x-30$. Enter the zeros separated by commas.
Question Help: $\square$ Video $\square$ Message instructor
Submit Question

Answer

Expert–verified

Hide Steps

Answer

Final Answer: The zeros of the function are $\boxed{2.5, 2, 0.75}$.

Steps

Step 1 ：Set the function equal to zero: $8x^{3}-42x^{2}+67x-30 = 0$.

Step 2 ：This is a cubic equation, so it might have up to three real roots.

Step 3 ：The roots of the function are the values of x for which the function equals zero.

Step 4 ：Calculate the roots of the function.

Step 5 ：The roots of the function are 2.5, 2, and 0.75.

Step 6 ：Final Answer: The zeros of the function are $\boxed{2.5, 2, 0.75}$.