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

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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)   (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 (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

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 - .

The solution is

Here's your graph:


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



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