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

Solution:

Given the number line;

The inequality;

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

Also;

$x+\frac{5}{2}<\sqrt{\frac{45}{4}}:x<\frac{3\sqrt{5}-5}{2}$

Combine the intervals;

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