They are the solutions for the reduced quadratic.
The graphs of the two equations have only one intersection point.
Yes and they do in factoring quadratic equations.Yes and they do in factoring quadratic equations.Yes and they do in factoring quadratic equations.Yes and they do in factoring quadratic equations.
A quadratic equation ax2 + bx + c = 0 has the solutions x = [-b +/- sqrt(b2 - 4*a*c)]/(2*a)
Yes FOIL method can be used with quadratic expressions and equations
They are the solutions for the reduced quadratic.
If they are quadratic equations then if their discriminant is less than zero then they have no solutions
There is no quadratic equation that is 'linear'. There are linear equations and quadratic equations. Linear equations are equations in which the degree of the variable is 1, and quadratic equations are those equations in which the degree of the variable is 2.
The graphs of the two equations have only one intersection point.
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.
Graphing
The quadratic formula is used today to find the solutions to quadratic equations, which are equations of the form ax^2 + bx + c = 0. By using the quadratic formula, we can determine the values of x that satisfy the quadratic equation and represent the points where the graph of the equation intersects the x-axis.
The two equations represent parallel lines.
Wolfram Alpha can solve not just quadratic equations, but all sorts of equations. Note that in this particular website, you can see the solution for free, but you need a paid subscription to show the steps. I am sure there are other websites that can help you as well; you may want to try a Web search for "quadratic equation", for example. On the other hand, you should definitely learn to solve quadratic equations on your own.
A system of equations will have no solutions if the line they represent are parallel. Remember that the solution of a system of equations is physically represented by the intersection point of the two lines. If the lines don't intersect (parallel) then there can be no solution.
There are several methods for solving quadratic equations, although some apply only to specific quadratic equations of specific forms. The methods include:Use of the quadratic formulaCompleting the SquareFactoringIterative methodsguessing
Yes and they do in factoring quadratic equations.Yes and they do in factoring quadratic equations.Yes and they do in factoring quadratic equations.Yes and they do in factoring quadratic equations.