SOLUTION: Find all roots of f(x)=2x^4-17x^3+49x2-23x-91, given that 7/2 and -1 are roots Thank you

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find all roots of f(x)=2x^4-17x^3+49x2-23x-91, given that 7/2 and -1 are roots Thank you      Log On


   

Question 58436: Find all roots of f(x)=2x^4-17x^3+49x2-23x-91, given that 7/2 and -1 are roots

Thank you
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = 2x^4 - 17x^3 + 49x^2 - 23x - 91
(x + 1) is a factor:
-1|....2....-17....49....-23....-91
........2....-19....68.....-91....0
(x + 1)(2x^3 - 19x^2 + 68x - 91) = f(x)
(x - 7/2) is a factor:
7/2|....2....-19....68....-91
.........2.....-12....26.....0
(x + 1)(x - 7/2)(2x^2 - 12x + 26) = f(x)
(x + 1)(x - 7/2)2(x^2 - 6x + 13) = f(x)
x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%286+%2B-+sqrt%28+36+-+52+%29%29%2F%282%29+
x+=+%286+%2B-+sqrt%28+-16+%29%29%2F%282%29+
Don't Exist
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C2x%5E4+-+17x%5E3+%2B+49x%5E2+-+23x+-+91%29