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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).
What is quadratic linear function?
It is a quadratic equation that normally has two solutions
What is true about the solutions of a quadratic equation when the radicand of the quadratic formula is a perfect square?
The two solutions are coincident.
How many real solutions can the quadratic formula give?
A quadratic equation can have either two real solutions or no real solutions.
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.
How many solutions will the equation 25 equals 2x squared 6x have?
The quadratic equation will have two solutions.
How can you tell from an equation if it is Quadratic?
One of its terms will be squared and it will have two solutions.
Does a quadratic equation has exactly one solution?
Normally it has two solutions but sometimes the solutions can be the same.
How many real solutions does a quadratic equation have if its discriminant is zero?
It will then have two equal real solutions
A positive discriminant means the quadratic equation will have how many solutions?
Two distinct real solutions.
How many solutions does a quadratic equation and an absolute value equation have?
They each typically have two solutions, a positive one and a negative one.
Could you ever have three solutions to a quadratic equation?
No. By definition, a quadratic equation can have at most two solutions. For a quadratic of the form ax^2 + bx + c, when the discriminant of a quadratic, b^2 - 4a*c is positive you have two distinct real solutions. As the discriminant becomes smaller, the two solutions move closer together. When the discriminant becomes zero, the two solutions coincide which may also be considered a quadratic with only one solution. When the discriminant is negative, there are no real solutions but there will be two complex solutions - that is those involving i = sqrt(-1).
