Question

How do you know that a Quadratic equation cannot be solved by factoring, but can be solved by using the quadratic formula?

Answer 1

If the discriminant isn't a perfect square, then you cannot solve the equation by factoring.

Answer 2

well really any quadratic equation can be solved by factoring or by quadratic formula

Answer 3

oh I meant factoring over the rationals

Answer 4

i have proved this

Answer 5

although it is hard to factor over the complex it is not impossible

Answer 6

Usually I try by factoring method if it fails then I resort to quadratic formula which works for ANY quadratic equation.

Answer 7

by "factor" I think they mean do so without the quadratic formula (ie find two numbers that multiply to this and add to that...etc)

Answer 8

usually people just try to factor over the integers then if that is not possible they result to the quadratic formula (or completing the square)

Answer 9

i can factor without the quadratic formula

Answer 10

lol well average people then

Answer 11

give me any quadratic and i will show you

Answer 12

For instance: x^2 + 3x + 5 this is not factorable so you have to use the quadratic formula and you will get a complex root.

Answer 13

not superhuman machines lol

Answer 14

lol

Answer 15

\[\left(x-\frac{-3}{2}-\frac{\sqrt{11}}{2}i\right)\left(x-\frac{-3}{2}+\frac{\sqrt{11}}{2}i\right)\]

Answer 16

we can use factor by grouping as i did in this file above

Answer 17

0.0 wow

Answer 18

cool!!...learnt something new today

Answer 19

i come up with that way

Answer 20

:)

Answer 21

i made a proof for the quadratic formula

Answer 22

but its run time is much longer than completing the square

Answer 23

so it almost useless

Answer 24

thank you for all the help ^.^