Hi,
I need help with this equation, i must solve it by factorising this quadratic equation.
27x^2 - 2x = 8
Help appreciated.
Tim
Hello, Moo!
As soon as you mention "Discriminant", you are no longer factoring.The discriminant is positive...
Sure, the solution is quite ugly, but it remains factorisable.
. . You are obviously invoking the Quadratic Formula.
I don't agree . . .But it's false to state what you said...
According to my understanding of "factorable", $\displaystyle x^2-4x + 6$ doesn't factor.
Sure, we can use the Quadratic Formula and get: .$\displaystyle x \;=\;2 \pm i\sqrt{5}$
We can say that we have two factors: .$\displaystyle \left(x - [2 + i\sqrt{5}]\right)\,\left(x - [2-i\sqrt{5}]\right) $
. . but I would not claim that we factored it.
If we include irrational and complex expressions, everything factors.
. . $\displaystyle x^4 + 1 \;=\;\left(x-\sqrt{i}\right)\left(x + \sqrt{i}\right)\left(x - i\sqrt{i}\right)\left(x + i\sqrt{i}\right) $
. . $\displaystyle x + 4 \;=\;\left(\sqrt{x} - 2i\right)\left(\sqrt{x}+2i\right)$
Oh, I think we just don't agree with the term "factorable"...
There will always be a way to factor it
But I'm not sure to get the reason why it is not factorable in your terms...
Your example of x²-4x+6 shows that we factored it... since we got two factors... whatever the way we used is, isn't it ?
There is also the property :
if a trinomial is factorable, then, it can be written the following way : c(x-a)(x-b).
Huh ?