## anonymous 5 years ago What are the solutions of x^2 - 3x +9 = 0

1. anonymous

Imaginary

2. anonymous

Thanks man.

3. anonymous

4. anonymous

Well not sarcastic i figured you were at least trying to help so i appreciate that. The problem is still confusing me though? :[

5. anonymous

You can either work it out with the quadratic formula or completing the square, but the graph does not cross the x axis, so both solutions are imaginary.

6. anonymous

But i did not get two solutions in the problem? :[ im just totally confused on how to solve it :/

7. anonymous

OK one second:

8. anonymous

$x^2 - 3x + 9 = 0$ $\iff \left(x-\frac{3}{2}\right)^2 - \left(\frac{3}{2}\right)^2 + 9 = 0$ $\iff \left(x-\frac{3}{2}\right)^2 = -\frac{27}{4}$ $\implies x-\frac{3}{2} = \pm \sqrt{\frac{-27}{4}}$

9. anonymous

Of course, you could equally just use the formula, but I think this way is more fun. Do you know how to carry on (mainly with the root) to get the imaginary/complex solution?

10. anonymous

I do not.

11. anonymous

Do you see how the working I posted works?

12. anonymous

Yeahh.....

13. anonymous

$\sqrt{\frac{-27}{4}} = \sqrt{-1}\cdot\sqrt{\frac{27}{4}} = i\cdot\frac{3\sqrt{3}}{2}$

14. anonymous

Again, it may be more 'standard' and easier to repeat if you use the quadratic formula instead, but it would still need you to take the root of a negative number.