Question

Solve x^2−x+6>0 algebraically. Write the solution in interval notation. If there is no solution, type ∅.Note: Use the ∪ symbol (not the letter U) found on the keyboard below if applicable.

Answer 1

Simplify the inequlaity x^2−x+6>0 for x.

`\begin{gathered} x^2-x+6>0 \\ x^2-2\cdot(1)/(2)\cdot x+(1)/(4)-(1)/(4)+6>0 \\ (x-(1)/(2))^2+(23)/(4)>0 \\ (x-(1)/(2))^2+(23)/(4)-(23)/(4)>0-(23)/(4) \\ (x-(1)/(2))^2>-(23)/(4) \end{gathered}`

Since above inequality is true for every value of x. Thus solution of equation is,

`(-\infty,\infty)`

Answer:

`(-\infty,\infty)`