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Q: Which method of solving quadratic equations should be used when only an estimated solution is necessary?

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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

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.

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 quadratic equation ax2 + bx + c = 0 has the solutions x = [-b +/- sqrt(b2 - 4*a*c)]/(2*a)

The term "discriminant" is usually used for quadratic equations. If the discriminant is zero, then the equation has exactly one solution.

ax3 + bx2 + cx x(ax2 + bx + c) you get one answer as 0.

A quadratic equation can have two real solutions, one real solution, or two complex solutions, none of them real.

so you can find the solution for the x-values. the x-intercepts are when the graph crosses the x-axis

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.

The functions of roots of 84 is that they help us get the solution of certain quadratic equations and therefore help us to plot the graphs correctly.

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.

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