Question

1) Quais são as soluções da equação 2x² – 7x – 4 = 0: *

a) 2 e 4
b) ½ e 4
c) – ½ e 4
d) –4 e ½

Answer 1

As soluções da equação de 2º grau são, x'=4 e x"=-1/2. Alternativa C!

Aplicando a fórmua de Bháskara, temos:

$\Delta=b^2-4ac\\\\\Delta=(-7)^2-4\cdot2\cdot(-4)\\\\\Delta=49+32\\\\\Large\boxed{\Delta=81}\\\\\\x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\x=\dfrac{-(-7)\pm\sqrt{81}}{2\cdot2}\\\\\Large\boxed{x=\dfrac{7\pm9}{4}}\\\\\\\boxed{\large\begin {array}{l}x'=\dfrac{7+9}{4}\\\\x'=\dfrac{16}{4}\\\\\Large\boxed{\boxed{x'=4}}\Huge\checkmark\end {array}}\quad\quad\boxed{\large\begin {array}{l}x"=\dfrac{7-9}{4}\\\\x"=\dfrac{-2}{4}\\\\\Large\boxed{\boxed{x"=-\dfrac{1}{2}}}\Huge\checkmark\end {array}}$

Portanto, S={4, -1/2}. Alternativa C!

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Bons estudos!