SOLUTION: P(x) = 4x4 − x3 − 8x2 + 18x − 4 Find all the zeros of the polynomial function. (Hint: First determine the rational zeros. Enter your answers as a comma-separated

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: P(x) = 4x4 − x3 − 8x2 + 18x − 4 Find all the zeros of the polynomial function. (Hint: First determine the rational zeros. Enter your answers as a comma-separated      Log On


   

Question 1001497: P(x) = 4x4 − x3 − 8x2 + 18x − 4
Find all the zeros of the polynomial function. (Hint: First determine the rational zeros. Enter your answers as a comma-separated list. Enter all answers including repetitions.)
x =
Write the polynomial as a product of its leading coefficient and its linear factors.
P(x) =
Answer by sidt36(1) About Me  (Show Source):
You can put this solution on YOUR website!
Hello;
Lets factor this and Proceed
.
Now the roots
4x -1 = 0
x = 1/4
x+ 2 = x = -2
Now lets Find the roots of the quadratic
Lets complete the square;
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B2+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A1%2A2=-4.

The discriminant -4 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -4 is + or - sqrt%28+4%29+=+2.

The solution is x%5B12%5D+=+%28--2%2B-+i%2Asqrt%28+-4+%29%29%2F2%5C1+=++%28--2%2B-+i%2A2%29%2F2%5C1+

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B2+%29


x = -2,1/4
( the real roots are)