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.
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.
Draw the graph of the equation. the solution is/are the points where the line cuts the x(horisontal) axis .
Is it possible for a quadratic equation to have no real solution? please give an example and explain. Thank you
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.
Three different kinds: none, one and infinitely many.
No, it must have two answers.
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.
If the discriminant of the quadratic equation is greater than zero then it will have two different solutions. If the discriminant is equal to zero then it will have two equal solutions. If the discriminant is less than zero then it will have no real solutions.
ax3 + bx2 + cx x(ax2 + bx + c) you get one answer as 0.
TWO linear equations with different slopes intersect in one point, regardlessof their y-intercepts. That point is the solution of the pair.However, this does not mean that three (or more) equations in two variables, even if they meet the above conditions, have a solution.
one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel
No. A quadratic may have two identical real solutions, two different real solutions, ortwo conjugate complex solutions (including pure imaginary).It can't have one real and one complex or imaginary solution.
If the equations or inequalities have the same slope, they have no solution or infinite solutions. If the equations/inequalities have different slopes, the system has only one solution.
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
The slopes (gradients) of the two equations are 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.
there is no linear equations that has no solution every problem has a solution