x2 - 25 = 0 is x2 = 25 thus x = 5 or x = -5, only 2 real solutions
Without an equal sign, that isn't an equation.If you mean x squared - 25 = 0, that's the same as x squared = 25; the solutions are 5 and -5.
x^2 - 25 is an expression, not an equation. An expression cannot have a solution.
A quadratic equation always has TWO (2) solutions. They may be different, the same, or non-existant as real numbers (ie they only exist as complex numbers).
It depends on the equation. Also, the domain must be such that is supports an infinite number of solutions. A quadratic equation, for example, has no real solution if its discriminant is negative. It cannot have an infinite number of solutions. Many trigonometric equations are periodic and consequently have an infinite number of solutions - provided the domain is also infinite. A function defined as follows: f(x) = 1 if x is real f(x) = 0 if x is not real has no real solutions but an infinite number of solutions in complex numbers.
C
Assuming a, b, and c are real numbers, there are three possibilities for the solutions, depending on whether the discriminant - the square root part in the quadratic formula - is positive, zero, or negative:Two real solutionsOne ("double") real solutionTwo complex solutions
They will have 2 different solutions or 2 equal solutions and some times none depending on the value of the discriminant within the quadratic equation
apex- real
The complex roots of an equation is any solution to that equation which cannot be expressed in terms of real numbers. For example, the equation 0 = x² + 5 does not have any solution in real numbers. But in complex numbers, it has solutions.
A quadratic equation always has TWO (2) solutions. They may be different, the same, or non-existant as real numbers (ie they only exist as complex numbers).
It has two complex solutions.
A quadratic equation can have two real solutions, one real solution, or two complex solutions, none of them real.
It depends on the equation. Also, the domain must be such that is supports an infinite number of solutions. A quadratic equation, for example, has no real solution if its discriminant is negative. It cannot have an infinite number of solutions. Many trigonometric equations are periodic and consequently have an infinite number of solutions - provided the domain is also infinite. A function defined as follows: f(x) = 1 if x is real f(x) = 0 if x is not real has no real solutions but an infinite number of solutions in complex numbers.
0 real solutions. There are other solutions in the complex planes (with i, the imaginary number), but there are no real solutions.
imaginary
They were discovered when Cardano solved the third degree equation. In the formulas that arose to solve the third degree equation, Cardano needed to take the square root of negative numbers and add them up in a certain way. The strange thing that happened was that the formulas used these complex numbers, even if the solutions to the equation where all real. This baffled the mathematicians of the time, because how could these strange numbers turn out to be "real"? Later this was considered totally correct, when the field of complex numbers was better undestood.
Here are a few: 0 = 1 x = x + 1 (subtract "x" on each side, and you get the previous one!) x2 = -1 (if you want real numbers; however, it has two solutions in the complex numbers) ln x = -1 (same as above: no solution in the real numbers, but it has a solution in the complex numbers) ln x = 0 (no solution, neither in the real numbers, nor in the complex numbers) 0x = 5
There are two types of numbers. The real number system that we use everyday for counting and money and such. There is also the imaginary or complex number system that is used to help evaluate the square roots of negative numbers. A 'real solution' generally means that the solution is one from the real number system. When solving an equation (especially at lower grade levels) the answer might be that there are no real solutions. However there might be complex solutions to the problem.
The number of solutions of a rational equation depends on the power (or degree) of the equation (that is, the highest power to which the variable is raised) and the domain. In the complex domain, each rational equation of power n has n solutions. It is, however, possible that two or more of these solutions are coincident - or "multiple zeros". In the real domain, the number of solutions can fall in pairs. So an equation of power 7 will always have 7 complex solutions but it can have 7, 5, 3 or 1 real solutions. (Real numbers are a subset of complex numbers). Another way of seeing this is through factorisation: The equation x3 + x2 - 10x + 8 = 0 can be factorised into (x + 1)*(x - 2)*(x - 4) = 0 Now the product of three numbers is 0 is any one of them is 0. That is, if x + 1 = 0 or if x - 2 = 0 or if x - 4 = 0 Thus the equation has the solutions: x = - 1, x = 2 or x = 4. The equation of order n can have at most n real binomial factors. (Any more and the biggest power of x would be bigger than n). And again, in the complex domain, using the binomial equation (and equivalents), it must have n binomial factors.