Question

Quais as raízes das funções y= x²-7x+10 e y= 3x²-7x+2?

Answer 1

Explicação passo-a-passo:

a) $\sf x^2-7x+10=0$

$\sf \Delta=(-7)^2-4\cdot1\cdot10$

$\sf \Delta=49-40$

$\sf \Delta=9$

$\sf x=\dfrac{-(-7)\pm\sqrt{9}}{2\cdot1}=\dfrac{7\pm3}{2}$

$\sf x'=\dfrac{7+3}{2}~\longrightarrow~x'=\dfrac{10}{2}~\longrightarrow~x'=5$

$\sf x"=\dfrac{7-3}{2}~\longrightarrow~x"=\dfrac{4}{2}~\longrightarrow~x"=2$

As raízes são $2$ e $5$

b) $\sf 3x^2-7x+2=0$

$\sf \Delta=(-7)^2-4\cdot3\cdot2$

$\sf \Delta=49-24$

$\sf \Delta=25$

$\sf x=\dfrac{-(-7)\pm\sqrt{25}}{2\cdot3}=\dfrac{7\pm5}{6}$

$\sf x'=\dfrac{7+5}{6}~\longrightarrow~x'=\dfrac{12}{6}~\longrightarrow~x'=2$

$\sf x"=\dfrac{7-5}{6}~\longrightarrow~x"=\dfrac{2}{6}~\longrightarrow~x"=\dfrac{1}{3}$

As raízes são $\dfrac{1}{3}$ e $2$