Question

A menor raiz da equação 2x² + 7x -15 = 0 é: *

a)1
b)2
c)3/2
d)1/2

Answer 1

$\Delta=b^2-4ac\\\Delta=7^2-4\cdot2\cdot(-15)\\\Delta=49+120\\ \Delta=169$

$x=\frac{-b\pm\sqrt{\Delta}}{2a}=\frac{-7\pm\sqrt{169}}{2\cdot2}=\frac{-7\pm13}{4}\\\\x'=\frac{-7+13}{4}=\frac{6^{:2}}{4_{:2}}=\frac{3}{2}\\\\x''=\frac{-7-13}{4}=\frac{-20}{4}=-5$

A menor das raízes é a negativa, ou seja -5.