Question

9. A partir da expressão x = -b ± √/2a, deduza a expressão ax² + bx + c = 0.

Answer 1

$\displaystyle \sf x=\frac{-b\pm\sqrt{\Delta}}{2a} \\\\\\ x = \frac{-b\pm\sqrt{b^2-4ac}}{2a} \\\\\\ 2a\cdot x= -b\pm\sqrt{b^2-4ac} \\\\ \left(2a\cdot x +b\right)^2 = \left(\pm\sqrt{b^2-4ac} \right)^2$

$\displaystyle \sf (2a\cdot x)^2+2\cdot (2a\cdot x)\cdot (b)+b^2 = b^2-4ac \\\\ 4a^2\cdot x^2+4a\cdot x\cdot b+b^2 = b^2-4ac \\\\ 4a^2\cdot x^2+4a\cdot x\cdot b+b^2 - b^2+4ac = 0 \\\\ 4a^2\cdot x^2+4a\cdot x\cdot b+4ac = 0 \ \ \div(4\cdot a) \\\\ \frac{4a^2\cdot x^2}{4a}+\frac{4a\cdot x\cdot b}{4a}+\frac{4ac}{4a} = \frac{0}{4a} \\\\\\ \huge\boxed{\sf a\cdot x^2+b\cdot x + c = 0 \ }\checkmark$