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**Solve the following quadratic equation. Use factorisation if possible.**

X

X

^{2}- 4X - 8 = 0Normally I wouldn't have trouble factorising a quadratic, but I have just been introduced to a new way to do it and I want to use this way to answer the question.

Here's how far I get, then I'm unsure what to do with the info I have.

**X**

Let [itex]\alpha[/itex] and [itex]\beta[/itex] be the roots of the equation.

(X-[itex]\alpha[/itex])(X-[itex]\beta[/itex]) = 0

Therefore

X

Or in another form;

X

Comparing coefficients.

[itex]\alpha[/itex]+[itex]\beta[/itex] = -[itex]\frac{b}{a}[/itex] = 4

[itex]\alpha[/itex][itex]\beta[/itex] = [itex]\frac{c}{a}[/itex] = -8

And now I'm confused about what I can do with this info to find the factors of the original quadratic.

Any help is appreciated!

Thanks.

^{2}- 4X - 8 = 0Let [itex]\alpha[/itex] and [itex]\beta[/itex] be the roots of the equation.

(X-[itex]\alpha[/itex])(X-[itex]\beta[/itex]) = 0

Therefore

X

^{2}- ([itex]\alpha[/itex]+[itex]\beta[/itex])X + [itex]\alpha[/itex][itex]\beta[/itex] = 0Or in another form;

X

^{2}+ [itex]\frac{b}{a}[/itex]X + [itex]\frac{c}{a}[/itex] = 0Comparing coefficients.

[itex]\alpha[/itex]+[itex]\beta[/itex] = -[itex]\frac{b}{a}[/itex] = 4

[itex]\alpha[/itex][itex]\beta[/itex] = [itex]\frac{c}{a}[/itex] = -8

And now I'm confused about what I can do with this info to find the factors of the original quadratic.

Any help is appreciated!

Thanks.