Question

Quais dos números-3, -2, 0, 1 e 5 são soluções da equação x ao cubo +2x -3=0?

Answer 1

$\large\boxed{\begin{array}{l}\underline{\rm Teorema\,das\,ra\acute izes\,racionais}\\\sf seja\,a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+\dots a_2x^2+a_1x+a_0=0\\\sf uma\,equac_{\!\!,}\tilde ao\,com\,coeficientes\,inteiros.\\\sf Se\,\dfrac{p}{q}~\acute e\,uma\,ra\acute iz~ent\tilde ao~p\,\acute e\,divisor\,de\,a_0\,e\,q\,divisor\,de\,a_n\\\sf nota\,caso\,a_n=1~as\,rai\acute zes(se\,houverem)\,s\tilde ao\,divisores\\\sf do\,termo\,independente.\end{array}}$

$\large\boxed{\begin{array}{l}\sf x^3+2x-3=0\\\sf candidatos\,a\,ra\acute izes:1,-1,3,-3.\\\sf testemos\,os\,valores\\\sf 1^3+2\cdot1-3=1+2-3=3-3=0\\\sf 1\,\acute e\,ra\acute iz.\\\sf da\,lista\,que\,nos\,foi\,dada,somente\,1\,satisfaz.\end{array}}$