Question

O conjunto solução da equação
X²-2x-15=0
A){-3,5}
B){-5,-3}
C) {3,5}
D){-5,3}

Answer 1

$\sf x^2-2x-15=0$

$\sf\Delta=b^2-4ac$

$\sf\Delta=(-2)^2-4\cdot1\cdot(-15)$

$\sf\Delta=4+60$

$\sf\Delta=64$

$\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}$

$\sf x=\dfrac{-(-2)\pm\sqrt{64}}{2\cdot1}$

$\sf x=\dfrac{2\pm8}{2}\begin{cases}\sf x_1=\dfrac{2+8}{2}=\dfrac{10}{2}=5\\\\\sf x_2=\dfrac{2-8}{2}=\dfrac{-6}{2}=-3\end{cases}$

$\boxed{\boxed{\sf S=\big\{-3;5\big\}}}\leftarrow\textsf{letra A}$