0
How would you know that your equation has infinite solutions without actually solving it?
Wiki User
∙ 6y ago
In some cases, a knowledge of the function in question helps. For example, when you have multiple equations, if you have more equations than variables you will usually have infinite solutions. Another example is that certain functions are known to be periodic, for instance the trigonometric functions - so an equation such as sin(x) = 1/2 may have infinite solution, due to the periodicity.
Wiki User
∙ 6y ago
Wiki User
∙ 6y agoSuppose the function is periodic, that is, f(x + p) = f(x) for all x and for some value p.
If f(x) = 0 has one solution then it has infinitely many.
It is, of course, possible for a non-periodic function to have infinitely many solutions.
Add your answer:
Earn +20 pts
How is solving an inequality different from solving an equation?
In solving an inequality you generally use the same methods as for solving an equation. The main difference is that when you multiply or divide each side by a negative, you have to switch the direction of the inequality sign. The solution to an equation is often a single value, but the solution to an inequality is usually an infinite set of numbers, such as x>3.
How would you know that your equation has no solutions without actually solving it?
It really depends on the type of equation. Sometimes you can know, from experience with similar equations. But in many cases, you have to actually do the work of trying to solve the equation.
Is it possible to have imaginary solutions when solving a polynomial equation?
yes
How many solutions does the equation 14x plus 2 equals 12x have?
That looks like a linear equation (no quadratic or higher terms), so you can expect it to have a single solution. However, actually solving the equation is not difficult; do it, to confirm this.
When solving a rational equation why is it necessary to perform a check?
It is important to check your answers to make sure that it doesn't give a zero denominator in the original equation. When we multiply both sides of an equation by the LCM the result might have solutions that are not solutions of the original equation. We have to check possible solutions in the original equation to make sure that the denominator does not equal zero. There is also the possibility that calculation errors were made in solving.
How is solving an inequality different from solving an equation?
In solving an inequality you generally use the same methods as for solving an equation. The main difference is that when you multiply or divide each side by a negative, you have to switch the direction of the inequality sign. The solution to an equation is often a single value, but the solution to an inequality is usually an infinite set of numbers, such as x>3.
How would you know that your equation has no solutions without actually solving it?
It really depends on the type of equation. Sometimes you can know, from experience with similar equations. But in many cases, you have to actually do the work of trying to solve the equation.
Is it possible to have imaginary solutions when solving a polynomial equation?
yes
Is satisfying an equation the same as solving it?
No. If an equation has many solutions, any one of them will satisfy it.
How do you know when an equation has infinitely many solutions or no solution?
They Are infinitely many solutions for an equation when after solving the equation for a variable(let us suppose x),we get the expression 0 = 0. Or Simply L.H.S = R.H.S For Ex. x+3=3+x x can have any value positive or negative, rational or irrational, it doesn't matter the sequence will be infinite. And No Solutions when after solving the equations the expression obtained is unequal For Ex. x+3=x+5 for every value of x, The Value in L.H.S And R.H.S. will differ. Hence It Has No Solutions.
How many solutions does the equation 14x plus 2 equals 12x have?
That looks like a linear equation (no quadratic or higher terms), so you can expect it to have a single solution. However, actually solving the equation is not difficult; do it, to confirm this.
When solving a rational equation why is it necessary to perform a check?
It is important to check your answers to make sure that it doesn't give a zero denominator in the original equation. When we multiply both sides of an equation by the LCM the result might have solutions that are not solutions of the original equation. We have to check possible solutions in the original equation to make sure that the denominator does not equal zero. There is also the possibility that calculation errors were made in solving.
What is a solution set?
is a set of all replacements that make an equation time in mathematics solution set is set of values which satisfies a given equation. For solving solutions you can get help from online Find Math Solutions.
How do you solve imaginary equations?
The answer depends on the nature of the equation. Just as there are different ways of solving a linear equation with a real solution and a quadratic equation with real solutions, and other kinds of equations, there are different methods for solving different kinds of imaginary equations.
In general when solving a radical equation should you first isolate the radical and then both sides?
It often helps to isolate the radical, and then square both sides. Beware of extraneous solutions - the new equation may have solutions that are not part of the solutions of the original equation, so you definitely need to check any purported solutions with the original equation.
What happens if you are checking a solution for the radical expression and find that it makes one of the denominators in the expression equal to zero?
Then it is not a solution of the original equation. It is quite common, when solving equations involving radicals, or even when solving equations with fractions, that "extraneous" solutions are added in the converted equation - additional solutions that are not solutions of the original equation. For example, when you multiply both sides of an equation by a factor (x-1), this is valid EXCEPT for the case that x = 1. Therefore, in this example, if x = 1 is a solution of the transformed equation, it may not be a solution to the original equation.
How would you go about solving a quadratic equation?
Write the quadratic equation in the form ax2 + bx + c = 0 then the roots (solutions) of the equation are: [-b ± √(b2 - 4*a*c)]/(2*a)
