Question

Para que valores reais de k a função f(x)= 2x²+5x+k+3 admite duas raízes reais e distintas?

Answer 1

$f(x)= 2x^2+5x+k+3$

$\Delta \ \textgreater \ 0 \\ \\ b^2 -4 \cdot a \cdot c\ \textgreater \ 0 \\ \\ 5^2-4 \cdot 2 \cdot (k+3)\ \textgreater \ 0 \\ \\ 25-8 \cdot (k+3)\ \textgreater \ 0 \\ \\ 25-8k-24\ \textgreater \ 0 \\ \\ -8k\ \textgreater \ 24-25 \\ \\ -8k\ \textgreater \ -1\\ \\ -k\ \textgreater \ -\dfrac{1}{8} \\ \\ -k \cdot (-1)\ \textgreater \ -\dfrac{1}{8} \cdot (-1) \\ \\ \boxed{k\ \textless \ \dfrac{1}{8} }$


Bons estudos!