- #1

Kyoma

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## Homework Statement

Is it true that all quadratic equations (ax

^{2}+bx+c) can be factorised into this form: (ax+b)(cx+d)?

I think so, but I'm not certain.

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- Thread starter Kyoma
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- #1

Kyoma

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Is it true that all quadratic equations (ax

I think so, but I'm not certain.

- #2

gb7nash

Homework Helper

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## Homework Statement

Is it true that all quadratic equations (ax^{2}+bx+c) can be factorised into this form: (ax+b)(cx+d)?

I think so, but I'm not certain.

If d is just some arbitrary number and you didn't accidentally duplicate your letters, then no.

Example:

y = x

So a = 1, b = -2, c = 1

So y = (x

a, c and d are fine, but you have a -1 instead of b.

- #3

SammyS

Staff Emeritus

Science Advisor

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As gb7nash said the coefficients a, b, and c, in (ax## Homework Statement

Is it true that all quadratic equations (ax^{2}+bx+c) can be factorised into this form: (ax+b)(cx+d)?

I think so, but I'm not certain.

So, can (ax

The answer is ... maybe.

If you allow q and s to be complex numbers, then the answer is yes.

If you restrict q and s to be real numbers, then you must have [itex]\sqrt{b^2-4ac}\ge0[/itex]

If q and s must be rational numbers, then you must have [itex]\sqrt{b^2-4ac}[/itex] be a perfect square.

If you allow q and s to be complex numbers, then the answer is yes.

If you restrict q and s to be real numbers, then you must have [itex]\sqrt{b^2-4ac}\ge0[/itex]

If q and s must be rational numbers, then you must have [itex]\sqrt{b^2-4ac}[/itex] be a perfect square.

This all assumes that a, b, and c are rational numbers.

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