SOLUTION: Use factor theorem to factorise the following quartic polynomial p(x).In each case write down the real roots of the equation p(0)=0 1=x^4-x^3-7x^2+x+6

Algebra ->  Equations -> SOLUTION: Use factor theorem to factorise the following quartic polynomial p(x).In each case write down the real roots of the equation p(0)=0 1=x^4-x^3-7x^2+x+6       Log On


   

Question 1163481: Use factor theorem to factorise the following quartic polynomial p(x).In each case write down the real roots of the equation p(0)=0
1=x^4-x^3-7x^2+x+6

Found 2 solutions by josgarithmetic, solver91311:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Not well written. Where is p(x)? What is the "1=" and the "2=" ?

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


I'm quite certain you meant because .

Lead coefficient is 1, so all possible rational roots are integers.

Set of possible rational zeros are the positive and negative integer factors of the constant term, 6:



You must now test the possibles using synthetic division until you get a zero remainder indicating you have found a root. 

Try x = 1

      1 -1 -7  1  6
  1      1  0 -7 -6
     -------------- 
      1  0 -7 -6  0

We got a zero remainder so we know that 1 is a root and (x - 1) is a factor.  The other factor is (x³ - 7x - 6).

Note that the cubic factor has the same possible rational zeros as the original quartic.

Continue to use synthetic division until you either find the other three factors or you run out of possibles. If you run out of possibles before you find all four factors, then you know that the remaining factors are irrational or even complex.


John

My calculator said it, I believe it, that settles it