Question

2. Obtener las soluciones de las siguientes ecuaciones cuadráticas utilizando la fórmula general:

a. x^2+2x-8=0

b. 4x^2+12x-8=0

c. 〖5x〗^2+6x+1=0

d. 〖2x〗^2+5x-12=0

e. x^2-8x+16=0

Answer 1

A.

$x^{2}+2x-8=0\\ \\a=1; b=2 ;c=-8\\\\x=\frac{-b±\sqrt{b^{2}-4ac}}{2a}\\ \\Reemplazamos:\\\\ x=\frac{-2±\sqrt{2^{2}-4*1*-8}}{2*1}\\\\ x=\frac{-2±\sqrt{4+32}}{2}\\\\ x=\frac{-2±\sqrt{36}}{2}\\\\ x=\frac{-2±6}{2}\\\\x1=\frac{-2+6}{2}\\ \\x1=\frac{4}{2}\\ \\x1=2\\\\x2=\frac{-2-6}{2}\\ \\x2=\frac{-8}{2}\\ \\x2=-4$

B.

$4x^{2}+12x-8=0\\ \\a=4; b=12 ;c=-8\\\\x=\frac{-b±\sqrt{b^{2}-4ac}}{2a}\\ \\Reemplazamos:\\\\ x=\frac{-12±\sqrt{12^{2}-4*4*-8}}{2*4}\\\\ x=\frac{-12±\sqrt{144+128}}{8}\\\\ x=\frac{-12±\sqrt{272}}{8}\\\\ x=\frac{-12±16,5}{8}\\\\x1=\frac{-12+16,5}{8}\\ \\x1=\frac{4,5}{8}\\ \\x2=\frac{-12-16,5}{8}\\ \\x2=\frac{-28,5}{8}$

C.

$5x^{2}+6x+1=0\\ \\a=5; b=6 ;c=1\\\\x=\frac{-b±\sqrt{b^{2}-4ac}}{2a}\\ \\Reemplazamos:\\\\ x=\frac{-6±\sqrt{6^{2}-4*5*1}}{2*5}\\\\ x=\frac{-6±\sqrt{36-20}}{10}\\\\ x=\frac{-6±\sqrt{16}}{10}\\\\ x=\frac{-6±4}{10}\\\\x1=\frac{-6+4}{10}\\ \\x1=\frac{-2}{10}\\ \\x1=-0,2\\\\x2=\frac{-6-4}{10}\\ \\x2=\frac{-10}{10}\\ \\x2=-1$

D.

$2x^{2}+5x-12=0\\ \\a=2; b=5 ;c=-12\\\\x=\frac{-b±\sqrt{b^{2}-4ac}}{2a}\\ \\Reemplazamos:\\\\ x=\frac{-5±\sqrt{5^{2}-4*2*-12}}{2*2}\\\\ x=\frac{-5±\sqrt{25+96}}{4}\\\\ x=\frac{-5±\sqrt{121}}{4}\\\\ x=\frac{-5±11}{4}\\\\x1=\frac{-5+11}{4}\\ \\x1=\frac{6}{4}\\ \\x1=1,5\\\\x2=\frac{-5-11}{4}\\ \\x2=\frac{-16}{4}\\ \\x2=-4$

E.

$x^{2}-8x+16=0\\ \\a=1; b=-8 ;c=16\\\\x=\frac{-b±\sqrt{b^{2}-4ac}}{2a}\\ \\Reemplazamos:\\\\ x=\frac{-(-8)±\sqrt{(-8)^{2}-4*1*16}}{2*1}\\\\ x=\frac{8±\sqrt{64-64}}{2}\\\\ x=\frac{8±\sqrt{0}}{2}\\\\ x=\frac{8±0}{2}\\\\x1=\frac{8+0}{2}\\ \\x1=\frac{8}{2}\\ \\x1=4\\\\x2=\frac{-8-0}{2}\\ \\x2=\frac{-8}{2}\\ \\x2=-4$