Question

Qual o valor de K para que a função y = -x² +x + (k + 1), tenha raízes e diferentes ?

Answer 1

$y=-x^2+x+(k+1)\\-x^2+x+(k+1)=0\\\\a=-1\ \ \ \ \ \ \ \ b=1\ \ \ \ \ \ \ \ c=k+1\\\\\triangle=b^2-4ac\\\triangle=1-4\cdot(-1)\cdot(k+1)\\\triangle=1+4\cdot(k+1)\\\triangle=1+4k+4\\\triangle=4k+5\\\\Para\ duas\ ra\'izes\ diferentes\ temos\ que\ \triangle\ \textgreater \ 0$

$4k+5\ \textgreater \ 0\\4k\ \textgreater \ -5\\\\k\ \textgreater \ -\dfrac{5}{4}$

Answer 2

Bom dia

-x² + x + (k + 1) 

delta
d² = 1 + 4*(k + 1)
d² = 4k + 5

duas raízes diferentes 

delta > 0

d² > 0

4k + 5 > 0
4k > -5
k > -5/4