Question

The graph below shows the solutions to which inequality?-6 -5 -4 -3 -2 -1 0 1OA. x2-5x+ 5 > 0OB. x2-5x+ 5 ≤0OC. x2 + 5x-5 <0OD. x2 + 5x -5>0

Answer 1

Given the number line;

The inequality;

`x^2+5x-5<0`
`\begin{gathered} \text{ complete the square;} \\ \\ x^2+5x-5=(x+(5)/(2))^2-(45)/(4) \\ \\ (x+(5)/(2))^2-(45)/(4)<0 \\ \\ (x+(5)/(2))^2-(45)/(4)+(45)/(4)<0+(45)/(4) \\ \\ (x+(5)/(2))^2<(45)/(4) \\ \\ -\sqrt{(45)/(4)}(-3√(5))/(2)-(5)/(2) \\ \\ -\sqrt{(45)/(4)}(-3√(5)-5)/(2) \end{gathered}`

Also;

`x+(5)/(2)<\sqrt{(45)/(4)}:x<(3√(5)-5)/(2)`

Combine the intervals;

[tex]\frac{-3\sqrt{5}-5}{2}Thus, the line graph is;