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
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only possible rational roots for q(x) are 1 and -1 ...
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 $\displaystyle p(x)=2x^4+5x^3-2x-5$ $\displaystyle p(x)=0$ $\displaystyle 2x^4+5x^3-2x-5=0$ $\displaystyle x^3(2x+5)-(2x+5)=0$ $\displaystyle (2x+5)(x^3-1)=0$ $\displaystyle (2x+5)(x-1)(x^2+x+1)=0$ ...and so on
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
Originally Posted by hoger hi can you explain for me I dont undrestand it . thank uou rational root theorem
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 $\displaystyle x^2+x+1=0$ from my earlier post using the quadratic formula.
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