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Q: How do you know if a quadratic equation will have one two or no solutions How do you find a quadratic equation if you are only given the solution Is it possible to have different quadratic equation?

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Yes it is possible. The solutions for a quadratic equation are the points where the function's graph touch the x-axis. There could be 2 places to that even if the graph looks different.

No because quadratic equations only have 2 X-Intercepts

In the graph of a quadratic equation, the plotted points form a parabola. This parabola usually intersects the X axis at two different points. Those two points are also the two solutions for the quadratic equation. Alternatively: Quadratic equations are formed by multiplying two linear equations together. Each of the linear equations has one solution - multiplying two together means that the solution for either is also a solution for the quadratic equation - hence you get two possible solutions for the quadratic unless both linear equations have exactly the same solution. Example: Two linear equations : x - a = 0 x - b = 0 Multiplied together: (x - a) ( x - b ) = 0 Either a or b is a solution to this quadratic equation. Hence most often you have two solutions but never more than two and always at least one solution.

Is it possible for a quadratic equation to have no real solution? please give an example and explain. Thank you

Yes it is quite possible

No, it must have two answers.

An inconsistent equation (or system of equations) is one that has no possible solutions.

yes

When the equation is a polynomial whose highest order (power) is 2. Eg. y= x2 + 2x + 10. Then you can use quadratic formula to solve if factoring is not possible.

Yes. For example, the equation x2 = 2, which in standard form is x2 - 2 = 0, has the two solutions x = square root of 2, and x = minus square root of 2.

If you mean 2x^2 -3x +8 = 0 then the discriminant works out as -55 which is less than 0 meaning that the equation has no real roots and so therefore no solutions are possible.

Yes and yes. eg x = y + 1 has an infinite number of solutions, and {sin(x) + cos(x) = 2} does not have a solution.

Yes, that is often possible. It depends on the equation, of course - some equations have no solutions.

None because without an equality sign the given expression is not an equation and so therefore no solutions are possible.

yes

The roots of an equation means the solutions of an equation. Different methods have been developed for different kinds of equation. It is not possible to give an overview in one or two paragraphs, but in simpler cases, the same operation is done on both sides of the equation, with the aim of "isolating" the variable you are solving for, that is, having it alone on one side. In some complicated cases, no "explicit" solutions exist, and "numerical" solutions have to be used; this basically means using trial-and-error.

There is no such thing as a quadric equation. The nearest word is quartic which is an equation involving the fourth power of the independent variable. It is unlikely that you will have come across that. It is possible that you might be wanting to refer to a quadratic equation, which is the equation of a parabola. That being the case, they two represent the same thing.

An inconsistent equation (or system of equations) is one that has no possible solutions. That is precisely why we call it inconsistent; there is no solution set that can be substituted for its variable or variables that will make the equation (or system) true.

No. Well, it depends what you mean with "any quadratic equation". The quadratic formula can solve any equation that can be converted to the form: ax2 + bx + c = 0 Note that it involves only a single variable. There are other limitations as well; for example, no additional operations. If a variable, or the square of a variable, appears in the denominator (1/x, or 1/x2), then some might say that it is "quadratic", but it might no longer be possible to convert the equation into the standard form named above. Similarly, if you have additional operations such as square roots or higher roots, trigonometric functions, etc., it might not be possible to convert the equation into a form that can be solved by the quadratic formula.

Yes, it is possible.

Using the discriminant formula for a quadratic equation k has a value of 8/25 or maybe 0.

Without an equality sign the given terms can't be considered to be an equation and so therefore no solutions are possible.

-0.82 , -4.82

Definitely.The equation [ x^2 = 4 ] has two solutions.x = +2x = -2The square root of any number can be a positive number or its negative. The solution for a quadratic equation often has two different values. However having two different values is still a single solution.

A single linear equation in two variables has infinitely many solutions. Two linear equations in two variables will usually have a single solution - but it is also possible that they have no solution, or infinitely many solutions.