SOLUTION: Find all solutions to the equation 6x^6-19x^5-47x^4+146x^3-150x^2-20x+48=0 I got x=4, x=3, x=-1/2, x=2/3. I got 2 other solutions but I am positive they are not correct. If some

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find all solutions to the equation 6x^6-19x^5-47x^4+146x^3-150x^2-20x+48=0 I got x=4, x=3, x=-1/2, x=2/3. I got 2 other solutions but I am positive they are not correct. If some      Log On


   

Question 1009928: Find all solutions to the equation 6x^6-19x^5-47x^4+146x^3-150x^2-20x+48=0
I got x=4, x=3, x=-1/2, x=2/3. I got 2 other solutions but I am positive they are not correct. If someone could show me the steps and verify my solutions are correct and help me find the other two solutions I would really appreciate it. I know I should have 6 solutions all together but I went wrong somewhere and can't figure out where. Thank you!
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
you are correct:
highlight%28x=4%29, highlight%28x=3%29, highlight%28x=-1%2F2%29, highlight%28x=2%2F3%29 are real solutions
when you factor completely your equation, you get
%28x-4%29+%28x%2B3%29+%282x%2B1%29+%283x-2%29+%28x%5E2-2x%2B2%29+=+0
and you have two more complex solutions when %28x%5E2-2x%2B2%29+=+0 and they are:
x%5E2-2x%2B2+=+0...use quadratic formula
x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29+
x+=+%282+%2B-+sqrt%28+4-8+%29%29%2F2+
x+=+%282+%2B-+sqrt%28+-4+%29%29%2F2+
x+=+%282+%2B-+2i%29%2F2+
x+=+%281+%2B-+i%29+
solutions:
highlight%28x+=+1-i%29
highlight%28x+=+1%2Bi%29