Find all zeros of p(x), real or imaginary. p(x) = x^{4} + 6x^{3} + 6x^{2} -18x -27 List all of the possible rational zeros according to the rational z

Lewis Harvey

Lewis Harvey

Answered question

2021-05-01

Find all zeros of p(x), real or imaginary. p(x)=x4+6x3+6x218x27 List all of the possible rational zeros according to the rational zero theorem and state the values for C, A, B and D in the following partial factorization of p(x)=(xc)(x3+Ax2+Bx+D) State the exact answer and a decimal approximation of each zero to the tenths place

Answer & Explanation

gotovub

gotovub

Skilled2021-05-02Added 98 answers

Step 1
Zeros of a polynomial:
p(x)=x4+6x3+6x218x27
To find zeros of a polynomial we need to put p(x)=0 and then simplify the polynomial in factor form.
Step 2
x4+6x3+6x218x27=0
x4+3x3+3x3+9x23x29x9x27=0
x3(x+3)+3x2(x+3)3x(x+3)9(x+3)=0
(x+3)(x3+3x23x9)=0
(x+3)(x2(x+3)3(x+3))=0
(x+3)(x+3)(x23)=0
(x+3)(x3)(x+3)(x3)=0
The zeros are (x+3)=0. x=-3
(x-3)=0. x=3
(x+3)=0.x=3
(x3)=0.x=3
The zeros are x=3,3,3,3
=3,-3,1.7,-1.7
The values of A,B,C,D are 3,-3,-3,-9 respectively.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?