# Thread: solve equation

1. ## solve equation

polynomial p(x)=2x^4+5x^3-2x-5 and q(x)=x^4+x^3+2x^2+x+1 have nontrivial common divisor .solve equation p(x)=0 .

thank you

2. only possible rational roots for q(x) are 1 and -1 ...

3. Originally Posted by hoger
polynomial p(x)=2x^4+5x^3-2x-5 and q(x)=x^4+x^3+2x^2+x+1 have nontrivial common divisor .solve equation p(x)=0 .

thank you
$p(x)=2x^4+5x^3-2x-5$

$p(x)=0$

$2x^4+5x^3-2x-5=0$

$x^3(2x+5)-(2x+5)=0$

$(2x+5)(x^3-1)=0$

$(2x+5)(x-1)(x^2+x+1)=0$

...and so on

4. Originally Posted by skeeter
only possible rational roots for q(x) are 1 and -1 ...
hi
can you explain for me I dont undrestand it .
thank uou

5. Originally Posted by hoger
hi
can you explain for me I dont undrestand it .
thank uou
rational root theorem

6. Originally Posted by hoger
hi
can you explain for me I dont undrestand it .
thank uou
q(x) has no real roots.

q(x) and p(x) share an imaginary root. You'll find that root when you solve $x^2+x+1=0$ from my earlier post using the quadratic formula.