SOLUTION: P(x) = x^4 -2x^3 -4x^2+14x-5

Algebra ->  Real-numbers -> SOLUTION: P(x) = x^4 -2x^3 -4x^2+14x-5      Log On


   

Question 1133823: P(x) = x^4 -2x^3 -4x^2+14x-5
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4+-2x%5E3+-4x%5E2%2B14x-5+=0
x%5E4%2B2x%5E3-x%5E2+-4x%5E3-8x%5E2+%2B4x%2B5x%5E2%2B10x-5=0+
%28x%5E4%2B2x%5E3-x%5E2%29+-%284x%5E3%2B8x%5E2+-4x%29%2B%285x%5E2%2B10x-5%29=0+
x%5E2%28x%5E2%2B2x+-1%29+-4x%28x%5E2%2B2x+-1%29%2B5%28x%5E2%2B2x-1%29=0+
%28x%5E2+%2B+2+x+-+1%29%28x%5E2+-+4+x+%2B+5%29=0
use quadratic formula:
if x%5E2+%2B+2+x+-+1=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+
x+=+%28-2+%2B-+sqrt%28+4%2B4+%29%29%2F2+
x+=+%28-2+%2B-+sqrt%28+2%2A4%29%29%2F2+
x+=+%28-2+%2B-+2sqrt%28+2%29%29%2F2+
x+=+%28-1+%2B-+sqrt%28+2%29%29
solutions:
x+=+-1+%2B+sqrt%28+2%29 => approximately 0.4
x+=+-1+-+sqrt%28+2%29 =>approximately -2.4
and
if x%5E2+-+4+x+%2B+5=0

x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A5+%29%29%2F%282%2A1%29+

x+=+%284+%2B-+sqrt%28+16-20+%29%29%2F2+
x+=+%284+%2B-+sqrt%28+-4+%29%29%2F2+
x+=+%284+%2B-+2i%29%2F2+
x+=+%282+%2B-+i%29+
solutions:
x+=+2+%2B+i+
x+=+2+-+i+

+graph%28+600%2C+600%2C+-10%2C+10%2C+-25%2C+10%2C+x%5E4+-2x%5E3+-4x%5E2%2B14x-5%29+