1.) Why are there usually two solutions in quadratic equations?

2.) Under what situation would one or more solutions of a rational equation be unacceptable?

:confused:

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- August 8th 2005, 09:41 PMAngel007math
1.) Why are there usually two solutions in quadratic equations?

2.) Under what situation would one or more solutions of a rational equation be unacceptable?

:confused: - August 9th 2005, 05:38 AMCold
Hi

1) Why are there usually two solutions in quadratic equations?

I think it'd be a useful for you to look at your choice of words and ask;

Why usually and not always? What are solutions? Can a quadratic equation have no solutions?

What is a quadratic equation? Why equation and not expression? Is there a difference?

Is x^2 - 2x = 3x - 6 a quadratic equation? If so why?

Is x(x+2) = -4 a quadratic.

If I said any quadratic equation can be written as ax^2 + bx + c = 0 is this true? What would the above equations look like?

Think about factorising a^2 + bx + c into (cx + d)(ex + f).

Even if it was true why bother with the 0? Hint (think about the values of a and b that make a x b = 0)

Draw graphs of the equations that you know the solutions for. Does the shape of the graph suggest a reason why your statement is or isn't true?

Please note that these are just my**SUGGESTIONS**and are only one way to help you answer the question.

2) I'm not sure exactly what you mean but consider

x^2 - 5x + 6

___________ = (x - 3)

(x - 2)

It is true that (x - 2)(x - 3) = x^2 - 5x + 6 so what's the problem? Hint: look at different values for x such as 1, 2, 3. Does the right hand side always equal the left?

Hope this has been of some help. I've just qualified as a teacher and am trying to get some practice in before september!