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For solving a quadratic, you mean? Well, if you have real solutions you know that your quadratic has real numbers that make f(x) equal 0. For example, the quadratic f(x) = x^2 - x - 6 has -2 and 3 for solutions, because if you put in either of those two numbers for x, you get 0.
I don't know how far along in your math career you are, but there aren't really any quadratics with no solutions, just with no real solutions. Some quadratics require you to take the square root of a negative number to get a solution, which is acceptable, it's just not a real solution anymore.
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What is the Difference between an integer and a real number?
Integer numbers are a subset of real numbers. Real numbers may contain fractions.
Is the difference between two real numbers a real number?
Yes, I can't think of any way that a real number minus another real number would be complex or purely imaginary. My answer is yes.
Is a fraction a real solution or a non-real solution in algebra?
A fraction is just a number. It's as real as any whole number (or decimal).
What is the difference between real solutions and real roots when dealing with discriminant?
There is no difference between real solutions and real roots.
What is the difference between a real number line and a fake number line?
The graph of imaginary numbers takes two axes. A part for the real part and the i part.
