a quadratic equation that doesn't have any real solution (1 Viewer)

kuromusha · Apr 7, 2016

What does it mean when a quadratic equation that doesn't have any real solution?

Does it mean that the equation does not either the x or y axis or does that mean the equation is not well defined?

eyeseeyou · Apr 7, 2016

It means there are no real solutions

If you were to graph it, the parabola wouldn't hit the x axis

InteGrand · Apr 7, 2016

kuromusha said:
What does it mean when a quadratic equation that doesn't have any real solution?

Does it mean that the equation does not either the x or y axis or does that mean the equation is not well defined?

$\noindent (Assuming the coefficients are real) Graphically it means when you graph the quadratic, it won't cross/touch the $x$-axis. It means that no real number will satisfy the equation. E.g. consider the equation $x^2+1=0$. This has no real solutions because no real number $x$ satisfies that. If you graph $y=x^2+1$, you'll see it is entirely above the $x$-axis. The only solutions to such quadratic equations will be (non-real) \emph{complex numbers}.$

You can read an intro to real and complex numbers here: https://www.mathsisfun.com/numbers/complex-numbers.html.

TheBondiTutor · Apr 9, 2016

Mathematicians from time to time like to use terms that in the context of mathematics has very specific meanings but to the rest of the world has a completely different meaning.

"Real Numbers" is one of these terms. In first year uni math (or 4 unit math) you'll come across what are known as imaginary number which, when combined with real numbers form complex numbers. If this is confusing, then I wouldn't worry as you don't really need to know the difference just yet.

Using InteGrand's example: the quadratics x^2 + 1 = 0 doesn't have any "real" solutions, it does have an "imaginary" solution of x = i (where i is the square root of -1 but again, you don't really need to know that just yet).

So next time you see the term "real" in a maths question, understand that mathematicians are extremely thorough when asking questions. The terms real, defined and undefined all have specific meanings but for someone in high school you can use the everyday meanings and they will work just fine.

si2136 · Apr 12, 2016

kuromusha said:
What does it mean when a quadratic equation that doesn't have any real solution?

Does it mean that the equation does not either the x or y axis or does that mean the equation is not well defined?

There are no real solutions. Which this leads to Ext. 2 Maths, which you learn about Complex Numbers.

eyeseeyou · May 13, 2016

Apparently complex numbers completes our whole number system

davidgoes4wce · May 13, 2016

$$ The discriminant would be less than 0.$

$$ The function does not have any x-axis solutions.$

$$ Given the formula for the roots is $ x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$If the discriminant $ b^2-4ac <0,$ then there are no solutions$

a quadratic equation that doesn't have any real solution (1 Viewer)

kuromusha

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eyeseeyou

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InteGrand

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TheBondiTutor

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eyeseeyou

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