• Matéria: Matemática
  • Autor: Katirltfm
  • Perguntado 6 anos atrás

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

Respostas

respondido por: Anônimo
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

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