Examples of Math Problems: Find the complex zeros of each polynomial function. write f in factored form. f(x)= x^3- 8x^2+ 25x-26

Tuesday, August 13, 2013

Find the complex zeros of each polynomial function. write f in factored form. f(x)= x^3- 8x^2+ 25x-26

f(x)= x^3- 8x^2+ 25x-26

working with the expression...

x^3- 8x^2+ 25x-26=
x^3- 8x^2+12x +13x-26=
x(x^2-8x+12)+13(x-2)=
x(x-2)(x-6)+13(x-2)
(x-2)(x^2-6x+13)
now a=1,b=-6, c=13

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation ax%5E2%2Bbx%2Bc=0

(in our case 1x%5E2%2B-6x%2B13+=+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

.

The discriminant -16 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 -16 is + or - sqrt%28+16%29+=+4