0
How do you know if a quadratic equation will have more than one solutions?
Wiki User
∙ 14y ago
Write the quadratic equation in the standard form: ax2 + bx + c = 0
Then calculate the discriminant = b2 - 4ac
If the discriminant is greater than zero, there are two distinct real solutions.
If the discriminant is zero, there is one real solution.
If the discriminany is less than zero, there are no real solutions (there will be two distinct imaginary solutions).
Wiki User
∙ 14y ago
Add your answer:
Earn +20 pts
Why are there usually two solutions to a quadratic equation?
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.
What does it mean in algebra to complete the square?
A quadratic equation can be solved by completing the square which gives more information about the properties of the parabola than with the quadratic equation formula.
The set of values that makes a statement true?
If the statement is a mathematical equation, than those values are its "solutions". The number of them depends on the equation. There may be only one, more than one, or no solutions at all.
What is the difference between quadratic function and quadratic formula?
A quadratic function is a function where a variable is raised to the second degree (2). Examples would be x2, or for more complexity, 2x2+4x+16. The quadratic formula is a way of finding the roots of a quadratic function, or where the parabola crosses the x-axis. There are many ways of finding roots, but the quadratic formula will always work for any quadratic function. In the form ax2+bx+c, the Quadratic Formula looks like this: x=-b±√b2-4ac _________ 2a The plus-minus means that there can 2 solutions.
How do you find the equation of a parabola if you know the equation of the tangent that touches it?
You need more than one tangent to find the equation of a parabola.
Is it possible for a quadratic equation to have more than 2 solutions?
No because quadratic equations only have 2 X-Intercepts
How can you tell how many solutions a quadratic equation will have without solving it?
A quadratic equation can have a maximum of 2 solutions. If the discriminant (b2-4ac) turns out to be less than 0, the equation will have no real roots. If the Discriminant is equal to 0, it will have equal roots. But, if the discriminant turns out to be more than 0,then the equation will have unequal and real roots.
Why Do you Study linear equations?
we study linear equation in other to know more about quadratic equation
Can a math problem have more than one answer?
Yes, it can. For example, if you are solving a quadratic equation, the curve could cross the x-axis in more than one place, thus the equation would have two solutions, a cubic equatuion can have 3 solutions, an equation with a power of four in it can have four solutions, etcetera.
What solution does a negative discriminant have?
In basic mathematics, a quadratic equation with a negative discriminant has no solutions. However, at a more advanced level you will learn that it has two solutions which form a complex conjugate pair.
Why are there usually two solutions to a quadratic equation?
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.
What is the value of coefficient a in the quadratic equation?
The answer depends on the quadratic equation. And since you have not bothered to provide that crucial bit of information, I cannot provide a more useful answer.The answer depends on the quadratic equation. And since you have not bothered to provide that crucial bit of information, I cannot provide a more useful answer.The answer depends on the quadratic equation. And since you have not bothered to provide that crucial bit of information, I cannot provide a more useful answer.The answer depends on the quadratic equation. And since you have not bothered to provide that crucial bit of information, I cannot provide a more useful answer.
What does it mean in algebra to complete the square?
A quadratic equation can be solved by completing the square which gives more information about the properties of the parabola than with the quadratic equation formula.
What is a quadratic eqation?
A quadratic equation is an equation where the highest exponent on the variable is 2. For example, the equation, y=2x2+3x-2 is a quadratic equation. The equation y=2x is not quadratic because the highest exponent on x is 1. (If there is no exponent on an x, then the exponent is 1.) The equation, y=x3+3x2-2 is not quadratic because the highest exponent is three. On a graph, a quadratic equation looks like a U or and upside down U. Here are some more example of quadratic equations: y=x2 y=3x2+2x-3 y=x2+5
The Square of a number is 5 more than 4 times the number. Find the number that makes the sentence true.?
This is a quadratic equation which will have two solutions: X2 = 4x+5 Rearrange the equation: x2-4x-5 = 0 Factor the equation: (x+1)(x-5) = 0 So the solutions are: x = -1 or x = 5
Which values for a b or c can you not use the quadratic equation?
a = 0. That is because a = 0 implies that there is no quadratic term and so the equation is not a quadratic!There may be some who make claims depending on the value of the discriminant (which is b2-4ac). That is true only for elementary mathematics. In more advanced mathematics (complex analysis), the quadratic equation can be used in all cases except when a = 0: the value of the discriminant is irrelevant.a = 0. That is because a = 0 implies that there is no quadratic term and so the equation is not a quadratic!There may be some who make claims depending on the value of the discriminant (which is b2-4ac). That is true only for elementary mathematics. In more advanced mathematics (complex analysis), the quadratic equation can be used in all cases except when a = 0: the value of the discriminant is irrelevant.a = 0. That is because a = 0 implies that there is no quadratic term and so the equation is not a quadratic!There may be some who make claims depending on the value of the discriminant (which is b2-4ac). That is true only for elementary mathematics. In more advanced mathematics (complex analysis), the quadratic equation can be used in all cases except when a = 0: the value of the discriminant is irrelevant.a = 0. That is because a = 0 implies that there is no quadratic term and so the equation is not a quadratic!There may be some who make claims depending on the value of the discriminant (which is b2-4ac). That is true only for elementary mathematics. In more advanced mathematics (complex analysis), the quadratic equation can be used in all cases except when a = 0: the value of the discriminant is irrelevant.
When you square each side of an equation is the resulting equation equivalent to the original?
No. The resulting equation has more solutions. For example, x = 2 has only one solution and that is x = 2.butx2= 4, the squared equation, has two solutions: x = +2 and x = -2No. The resulting equation has more solutions. For example, x = 2 has only one solution and that is x = 2.butx2= 4, the squared equation, has two solutions: x = +2 and x = -2No. The resulting equation has more solutions. For example, x = 2 has only one solution and that is x = 2.butx2= 4, the squared equation, has two solutions: x = +2 and x = -2No. The resulting equation has more solutions. For example, x = 2 has only one solution and that is x = 2.butx2= 4, the squared equation, has two solutions: x = +2 and x = -2
