Every quadratic equation has two solutions.
If the quadratic expression that's equal to zero is a perfect square,
then the two solutions are equal, and they look like one solution.
Example:
x2 - 6x + 9 = 0
(x - 3)(x - 3) = (x - 3)2 = 0
x = 3
and
x = 3.
Draw the graph of the equation. the solution is/are the points where the line cuts the x(horisontal) axis .
No, it must have two answers.
They are the solutions for the reduced quadratic.
b^2 - 4ac, the discriminant will tell you that a quadratic equation may have one real solution( discriminant = 0 ) , two real solutions( discriminant > 0 ), or no real solutions( discriminant < 0 ).
Normally it has two solutions but sometimes the solutions can be the same.
Draw the graph of the equation. the solution is/are the points where the line cuts the x(horisontal) axis .
No, it must have two answers.
They are the solutions for the reduced quadratic.
b^2 - 4ac, the discriminant will tell you that a quadratic equation may have one real solution( discriminant = 0 ) , two real solutions( discriminant > 0 ), or no real solutions( discriminant < 0 ).
It has one real solution.
The term "discriminant" is usually used for quadratic equations. If the discriminant is zero, then the equation has exactly one solution.
Normally it has two solutions but sometimes the solutions can be the same.
Sum
The solution to a math problem involving a quadratic equation is the values of the variable that make the equation true, typically found using the quadratic formula or factoring.
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.
x2
A quadratic equation has only one distinct solution when its discriminant (the part of the equation under the square root in the quadratic formula) is zero. This occurs when the equation can be expressed in the form ( (x - r)^2 = 0 ), where ( r ) is the repeated root. In this case, the parabola touches the x-axis at a single point, indicating that there is only one unique solution. Thus, the equation has a double root, rather than two distinct solutions.