Question

What are the solutions of x^2 - 3x +9 = 0

Answer 1

Imaginary

Answer 2

Thanks man.

Answer 3

Sarcastic? :(

I didn't technically help you.

Answer 4

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

Answer 5

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.

Answer 6

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

Answer 7

OK one second:

Answer 8

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

Answer 9

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?

Answer 10

I do not.

Answer 11

Do you see how the working I posted works?

Answer 12

Yeahh.....

Answer 13

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

Answer 14

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.