Question

Quais são as raizes das equações de 2 ° grau completas abaixo? a) x² - 7x - 8 = 0
b) (x + 3) (x - 3) = 4x​

Answer 1

a)

$\sf x^2-7x-8=0$

$\sf \Delta=(-7)^2-4\cdot1\cdot(-8)$

$\sf \Delta=49+32$

$\sf \Delta=81$

$\sf x=\dfrac{-(-7)\pm\sqrt{81}}{2\cdot1}=\dfrac{7\pm9}{2}$

$\sf x'=\dfrac{7+9}{2}~\rightarrow~x'=\dfrac{16}{2}~\rightarrow~\red{x'=8}$

$\sf x"=\dfrac{7-9}{2}~\rightarrow~x"=\dfrac{-2}{2}~\rightarrow~\red{x"=-1}$

b)

$\sf (x+3)\cdot(x-3)=4x$

$\sf x^2-3^2=4x$

$\sf x^2-9=4x$

$\sf x^2-4x-9=0$

$\sf \Delta=(-4)^2-4\cdot1\cdot(-9)$

$\sf \Delta=16+36$

$\sf \Delta=52$

$\sf x=\dfrac{-(-4)\pm\sqrt{52}}{2\cdot1}=\dfrac{4\pm2\sqrt{13}}{2}$

$\sf x'=\dfrac{4+2\sqrt{13}}{2}~\rightarrow~\red{x'=2+\sqrt{13}}$

$\sf x"=\dfrac{4-2\sqrt{13}}{2}~\rightarrow~\red{x"=2-\sqrt{13}}$