Question

A equação x²-x=12

a) admite a raiz 1.
b) admite a raiz -3.
c) admite a raiz -4.
d) não admite raízes reais.

Answer 1

$x^{2} -x=12\to\\\\ x^{2} -x-12=0\\\\ a=1;b=-1;c=-12\\\\\\ \Delta=b^2-4ac\to \Delta=(-1)^2-4.1.(-12)\to \Delta=1+48\to \Delta=49\\\\ x' \neq x''\\\\\\ x= \frac{-b\pm \sqrt{\Delta} }{2a} \to x= \frac{-(-1)\pm \sqrt{49} }{2.1} \to x= \frac{1\pm 7 }{2} \to \\\\\\ x'= \frac{1+ 7 }{2} \to x'= \frac{8 }{2} \to x'=4\\\\\\ x''= \frac{1- 7 }{2} \to x''= \frac{-6 }{2} \to x''=-3\\\\\\\\ S=\{-3;4\}$



R.: b) admite a raiz -3.