factor x^(2)-3x+5

Question

factor  x^(2)-3x+5

hero · Answer

Hint: Find two numbers that multiply to get 5, but add to get 3. 
2nd Hint: If you fail to find the two numbers, the polynomial might be prime.

anonymous · Answer

use quadratic formula

boxman61 · Answer

i know how to do it but the factors of 5 are 5 and 1 which n no way add to 3

hero · Answer

Well, see if you can make them equal -3. If not, then the polynomial could be prime.

boxman61 · Answer

problem is im trying to find the x intercepts of a parabola... problem is $$y=-x ^{2}+3x-5$$

hero · Answer

Well, in that case, set y = 0, then complete the square.

boxman61 · Answer

did that... $$0=-x ^{2}+3x-5$$
multiply by -1
$$0=x ^{2}-3x+5$$
then factor to find x intercepts

hero · Answer

Ask yourself this question: 

Does an x-intercept exist?

hero · Answer

D = b^2 - 4ac

If the discriminant is negative, then no, there doesn't exist an x-intercept.

boxman61 · Answer

its a parabola... should have 2 x intercepts, a y intercept, a vertex, and a 5th point.
its a big U shaped graph

hero · Answer

It "should" , but there exists many parabolas that fail to intercept the x-axis. Trust me.

boxman61 · Answer

ok thanks