What Are Real Roots in Mathematics?

[Lim Y K]

Can someone explain to me what are real roots?

 

[symbolipoint]

Real numbers which satisfy a polynomial function or a rational function. REAL as contrast to COMPLEX numbers containing imaginary parts.

 

[Mentallic]

Can someone explain to me what are real roots?

If you graph the function and see it cut the x-axis at a certain position (or positions) then the x value is a real root of the function.

 

[mathman]

Real numbers which satisfy a polynomial function or a rational function. REAL as contrast to COMPLEX numbers containing imaginary parts.

The term can refer to roots of any function, not just polynomial or rational.

 

[HallsofIvy]

Strictly speaking, one talks about "roots" of an equation, not a function. The "zeroes" of a function, f, are the "roots" of the equation f(x)= 0.

Of course, the "real" roots of an equation are those roots that are real numbers as opposed to complex numbers.

 

[NovicePWizzard]

I'm probably just dumbing down what has already been said, however, I think an explanation should be simple.

When you graph an equation, usually a quadratic one (formed like so: ax²+bx+c=0) there are three possibilities of what the resulting parabola could do. It could cross the x axis, it could just touch the x-axis at a single point, or it could just not cross it. Where the touch points are, are the roots. Every quadratic has roots of some description. Whether these are real or complex is a different issue though. Real numbers are the ones we use day to day. 1, 2, 3, 4, 5 ect. Complex numbers are something I haven't had much of a chance to delve into as of yet, but I believe they rotate around √-1 or i. When there is no crossing of the x axis, it has complex roots, and you cannot "solve" it for x. However, in the other two cases, it has real roots as there are cases where the parabola touches the x axis.
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Hopefully that clears something up!

 

[symbolipoint]

I'm probably just dumbing down what has already been said, however, I think an explanation should be simple.

When you graph an equation, usually a quadratic one (formed like so: ax²+bx+c=0) there are three possibilities of what the resulting parabola could do. It could cross the x axis, it could just touch the x-axis at a single point, or it could just not cross it. Where the touch points are, are the roots. Every quadratic has roots of some description. Whether these are real or complex is a different issue though. Real numbers are the ones we use day to day. 1, 2, 3, 4, 5 ect. Complex numbers are something I haven't had much of a chance to delve into as of yet, but I believe they rotate around √-1 or i. When there is no crossing of the x axis, it has complex roots, and you cannot "solve" it for x. However, in the other two cases, it has real roots as there are cases where the parabola touches the x axis.
.
Hopefully that clears something up!

Almost. You usually/often CAN solve for x if not cross nor touch the x axis. The root or roots would be COMPLEX.

 

[HallsofIvy]

Almost. You usually/often CAN solve for x if not cross nor touch the x axis. The root or roots would be COMPLEX.

But the question was specifically about real roots of an equation.

 

[symbolipoint]

But the question was specifically about real roots of an equation.

The poster will soon be able to make the distinction.

 

[aikismos]

Here are two functions. A root of an equation (or zero of a function in this case) is graphically where we cross the line y=0 (aka the x-axis or the abscissa if you're really old school). Notice that $g$ crosses three times, but $f$ crosses only once. We say $g$ has three real roots, and $f$ only one. Why real? It turns out (and if you haven't studied the quadratic equation yet), that sometimes you have to take the square root of negative numbers to find what value makes the entire equation equal to zero. Roots with imaginary numbers in them are NOT real (complex like the others have said). My 2 cents are that if you're a beginner, think of it as where the curve crosses the x-axis until you understand things better.

 

[NovicePWizzard]

Almost. You usually/often CAN solve for x if not cross nor touch the x axis. The root or roots would be COMPLEX.

I mean that, but it might not have been clear... Thank you for helping to clarify!