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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.
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Why are there usually two solutions in quadratic equations and when do they only have 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.
Why quadratic equations have two solutions?
If the discriminant of b2-4ac of the quadratic equation is greater the 0 then it will have 2 solutions.
Do all linear quadratic systems have two solutions or one?
They will have 2 different solutions or 2 equal solutions and some times none depending on the value of the discriminant within the quadratic equation
What is the answer for this quadratic equation 2x2 - 3x - 90?
That's not an equation - it doesn't have an equal sign. Assuming you mean 2x2 - 3x - 90 = 0, you can find the solution, or usually the two solutions, of such equations with the quadratic formula. In this case, replace a = 2, b = -3, c = -90.
How many solutions to a quardratic equation?
A quadratic equation always has TWO (2) solutions. They may be different, the same, or non-existant as real numbers (ie they only exist as complex numbers).
