SOLUTION: given f(x)= {{{(x+1)(x^3-27)}}} find all zeros (real and imaginary)

Question 165304: given f(x)= find all zeros (real and imaginary)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given function

Plug in

Factor to get . Note: use the difference of cubes formula.

or or Set each individual factor equal to zero

Solve the first two equations to get or . These are the first two zeros

Now let's solve

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

or Break up the expression.

So the zeros of are or

which approximate to or

=======================================================

Answer:

So in total, the 4 zeros are: , , or

Which in decimal form are , , or
RELATED QUESTIONS
Given: {{{P(x)=x^3-3x^2+25x-75}}} Find all zeros real and... (answered by oscargut)

14. find all the real and imaginary zeros of f(x)=x cubed+xsquared+13x-15; given that 1... (answered by stanbon)

State the number of complex zeros, the possible number or real and imaginary zeros, and... (answered by Boreal)

Find all real and imaginary zeros of the following polynomial equation: m(x)=... (answered by stanbon)

4.how do I find all of the real and imaginary zeros for the polynomial function for... (answered by Alan3354)

Find all of the real and imaginary zeros for the polynomial function. 12) f(x) = x3 -... (answered by edjones)

Find all real and imaginary roots of: f(x) = x^3 - 2x -... (answered by MathLover1)

I am suppose to find the number of real zeros and the number of imaginary zeros for the... (answered by vasumathi)

Find all zeros for the function,the total number of zeros, the number of real zeros, and... (answered by ewatrrr)