Question

Formaţi ecuţia cu rădăcinile: ×1 = 1/3,

×2 = 1/5​​

Answer 1

Răspuns:

Explicație pas cu pas:

dupa Viete:  

$pentru~ecuatia~x^{2}+px+q=0,~avem~relatiile~lui~Viete~\left \{ {{x_{1}+x_{2}=-p} \atop {x_{1}*x_{2}=q}} \right.~deci~\left \{ {{-p=\frac{1}{3}+\frac{1}{5} } \atop {q=\frac{1}{3}*\frac{1}{5}}} \right. ~\left \{ {{-p=\frac{8}{15} } \atop {q=\frac{1}{15} }} \right.\\Obtinem~ecuatia~x^{2}-\frac{8}{15}x+\frac{1}{15}=0~|*15,~15x^{2} -8x+1=0$