Question

O que fazer em uma equação do segundo grau quando a raiz do delta de número decimal ?????????????????????????

Answer 1

Continue normalmente! Só teria problema caso achasse delta menor que zero, aí a equação do segundo grau não possui raízes reais (mas possui raízes complexas)

Exemplo:

$x^{2}-\dfrac{71}{10}x+\dfrac{7}{10}=0\\\\\\\Delta=b^{2}-4ac\\\\\Delta=(-\frac{71}{10})^{2}-4\cdot1\cdot(\frac{7}{10})\\\\\Delta=(\frac{5041}{100})-(\frac{28}{10})\\\\\Delta=\frac{5041-280}{100}\\\\\Delta=\frac{4761}{100}\\\\\sqrt{\Delta}=\sqrt{\frac{4761}{100}}=\frac{\sqrt{4761}}{\sqrt{100}}=\frac{69}{10}$

Então:

$x=\dfrac{-b\pm\sqrt{\Delta}}{2a}=\dfrac{-(-\frac{71}{10})\pm(\frac{69}{10})}{2}=\dfrac{71\pm69}{20}\\\\\\x'=\dfrac{71+69}{20}=\dfrac{140}{20}=7\\\\\\x''=\dfrac{71-69}{20}=\dfrac{2}{20}=\dfrac{1}{10}$
______________________

Exemplo de raiz inexata:

$x^{2}-3=0~~~\therefore~~~x^{2}+0x-3=0\\\\\Delta=b^{2}-4ac\\\Delta=0^{2}-4\cdot1\cdot(-3)\\\Delta=0+12\\\Delta=12\\\Delta=4\cdot3\\\sqrt{\Delta}=\sqrt{4}\cdot\sqrt{3}\\\sqrt{\Delta}=2\cdot\sqrt{3}\\\sqrt{\Delta}=2\sqrt{3}\\\\x=\dfrac{-b\pm\sqrt{\Delta}}{2a}=\dfrac{0\pm2\sqrt{3}}{2}=\pm\dfrac{2\sqrt{3}}{2}=\pm\sqrt{3}\\\\\\\boxed{\boxed{x'=-\sqrt{3}~~~~x''=\sqrt{3}}}$