Question

Me ajude, imagem abaixo :

Answer 1

Resposta:

a)

$x^{2} -5x+6=0\\ \\ coeficientes\\ \\ a=1\\ b=-5\\ c=6\\ \\ \Delta=b^2-4ac\\ \Delta=(-5)^2-4(1)(6)\\ \Delta=25-24\\ \Delta=1\\ \\ x=\dfrac{-b\pm\sqrt{\Delta} }{2a}\\ \\ \\ x=\dfrac{-(-5)\pm\sqrt{1}}{2(1)}=\dfrac{5\pm1}{2}\\ \\\\ x'=\dfrac{5-1}{2}=\dfrac{4}{2}=2\\ \\ \\ x"=\dfrac{5+1}{2}=\dfrac{6}{2}=3\\ \\\boxed{ S=\{2,3\}}$

b)

$2x^2+x-6=0\\ \\ coeficientes\\ \\ a=2\\ b=1\\ c=-6\\ \\ \Delta=b^2-4ac\\ \Delta=1^2-4(2)(-6)\\ \Delta=1+48\\ \Delta=49$

$x=\dfrac{-b\pm\sqrt{\Delta} }{2a}\\ \\ \\ x=\dfrac{-1\pm\sqrt{49} }{2(2)}=\dfrac{-1\pm7}{4}\\ \\ \\ x'=\dfrac{-1-7}{4}=-\dfrac{8}{4}=-2\\ \\ \\ \\ x"=\dfrac{-1+7}{4}=\dfrac{6}{4}=\dfrac{3}{2}\\ \\ \\ \boxed{S=\{-2, \dfrac{3}{2}\}}$