SOLUTION: Can you help me to solve these 1. Find all zeros, both real and complex, of f(x)=x3-8x2 + 25x - 26 (3 and 2 are exponent) and write the polynomial in factored form.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Can you help me to solve these 1. Find all zeros, both real and complex, of f(x)=x3-8x2 + 25x - 26 (3 and 2 are exponent) and write the polynomial in factored form.       Log On


   

Question 119078: Can you help me to solve these
1. Find all zeros, both real and complex, of f(x)=x3-8x2 + 25x - 26 (3 and 2 are exponent) and write the polynomial in factored form.
Answer by chitra(359) About Me  (Show Source):
You can put this solution on YOUR website!
The given equation is: f(x)= x%5E3-+8x%5E2+%2B+25x+-+26+

To find the zeros of the given polynomial, we go in for the trail and error method.

when we plug in x = 2 in the above equation we find that it is one of the zeros of the polynomial.
hence the other roots are found by the method of synthetic division.

2|1 - 8 25 -26
0 2 -12 26
-----------------------
1 -6 13 |0
(x - 2)(x^2 - 6x + 13)

one root is = 2
and the other 2 roots are found by solving the quadratic equation, using the formula

x+=+%28-%28-6%29%29%2B-+sqrt%28+36-52+%29%29%2F%282%29+

x+=+%286+%2B-+isqrt%2816%29%29%2F%282%29

x+=+%286+%2B-+4i%29%2F2+

x+=+3+%2B-2i+

thus the other 2 roots.