Question

qual a resposta da equação 4× ao quadrado +12× -7 =0

Answer 1

Dada a equação:

$\mathsf{4x^2+12x-7=0}$

Aplicando a solução de uma equação do 2ª grau, onde:

$\mathsf{a=4\:;\:b=12\:;\:c=-7}$

 $\mathsf{x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}\\\\\\\mathsf{x=\dfrac{-12\pm \sqrt{12^2-4\cdot 4\cdot \left(-7\right)}}{2\cdot 4}}\\\\\\\mathsf{x=\dfrac{-12\pm \sqrt{144+112}}{8}}\\\\\\\mathsf{x=\dfrac{-12\pm \sqrt{256}}{8}}\\\\\\\mathsf{x=\dfrac{-12\pm 16}{8}}\\\\\\\mathsf{x=\dfrac{-3\pm 4}{2}}$

Logo, as soluções são:

◾ $\mathsf{x_1=\dfrac{-3+4}{2}=-\dfrac{1}{2}}$

◾ $\mathsf{x_2=\dfrac{-3-4}{2}=-\dfrac{7}{2}}$

$\boxed{\mathsf{S=\left\{x\in \mathbb{R}\:,\:x=\dfrac{1}{2}\:ou\:x=-\dfrac{7}{2}\right\}}}\: \: \checkmark$