Question

1) x^2+2mx-3m^2=0


2)3x^2-2xp+p^2/3=0

Responda aí pfv essas duas questões,na forma de fatoração?

Answer 1

1)

$x^2+2mx-3m^2=0\\\\\\a=1\:;\:b=2m\:;\:c=-3m^2\\\\\\x=\dfrac{-b\pm\sqrt{\Delta }}{2a}\\\\x=\dfrac{-b\pm \sqrt{b^2-4ac\:}}{2a}\\\\x=\dfrac{-2m\pm \sqrt{\left(2m\right)^2-4\cdot \:1\cdot \:\left(-3m^2\right)}}{2\cdot 1}\\\\x=\dfrac{-2m\pm \sqrt{4m^2+12m^2}}{2}\\\\x=\dfrac{-2m\pm \sqrt{16m^2}}{2}\\x=\dfrac{-2m\pm 4m}{2}\\\\x=-m\pm 2m\\\\\bold{x_1=-m+2m\:=m}\\\bold{x_2=-m-2m\:=3m}\\\\\\\boxed{\bold{S=\left\{m,\:3m\right\}}}$

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2)

$3x^2-2xp+\dfrac{p^2}{3}=0\\\\\\a=3\:;\:b=-2p\:;\:c=\dfrac{p^2}{3}\\\\\\x=\dfrac{-b\pm\sqrt{\Delta }}{2a}\\\\x=\dfrac{-b\pm \sqrt{b^2-4ac\:}}{2a}\\\\x=\dfrac{-\left(-2p\right)\pm \sqrt{\left(-2p\right)^2-\left(4\cdot 3\cdot \dfrac{p^2}{3}\right)}}{2\cdot 3}\\\\x=\dfrac{2p\pm \sqrt{4p^2-4p^2}}{6}\\\\x=\dfrac{2p\pm \sqrt{0}}{6}\\\\x=\dfrac{2p}{6}\\\\\bold{x=\dfrac{p}{3}}\\\\\\\boxed{\bold{S=\left\{x\in \mathbb{R},\:x=\dfrac{p}{3}\right\}}}}$