Question

Sem resolver as equações, determine a soma(s) e o produto(p) de suas raízes

a) X²-5X+6=0
b) X²+2X-8=0 ​

Answer 1

Resposta:

$x^2-5x+6=0\\\\x_{1,\:2}=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:1\cdot \:6}}{2\cdot \:1}\\\\x_{1,\:2}=\frac{-\left(-5\right)\pm \:1}{2\cdot \:1}\\\\x_1=\frac{-\left(-5\right)+1}{2\cdot \:1},\:x_2=\frac{-\left(-5\right)-1}{2\cdot \:1}\\\\x=3\\x=2$

$x^2+2x-8=0\\\\x_{1,\:2}=\frac{-2\pm \sqrt{2^2-4\cdot \:1\cdot \left(-8\right)}}{2\cdot \:1}\\\\x_{1,\:2}=\frac{-2\pm \:6}{2\cdot \:1}\\\\x_1=\frac{-2+6}{2\cdot \:1},\:x_2=\frac{-2-6}{2\cdot \:1}\\\\x=2\\x=-4$

$-4*2= -8$