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How many solutions are there if the discriminant of the equation is positive?
There are two distinct real solutions.
A positive discriminant means the quadratic equation will have how many solutions?
Two distinct real solutions.
How many real solutions does the following quadratic equation have by using the discriminant?
If the discriminant > 0 then 2 distinct real solutions.If the discriminant = 0 then 1 double real solution.If the discriminant < 0 then no real solutions (though there are two complex solutions).
Can two parabolas of the form with different vertices have the same axis of symmetry?
The form is not specified in the question so it is hard to tell. But two parabolas with different vertices can certainly have the same axis of symmetry.
Does every quadratic equation have two distinct real numbers in its solution set?
Nope. Consider x2+0x+1=0. This means x2+1=0. This has two solutions, but they are complex numbers: +i and -i, where i is the squareroot of -1. How about x2+0x+0=0? This means x2=0. This has two solutions, sure, but they aren't distinct. In this case, x=0 for both solutions, so we just consider them one solution.
How many solutions are there if the discriminant of the equation is positive?
There are two distinct real solutions.
A positive discriminant means the quadratic equation will have how many solutions?
Two distinct real solutions.
If the discriminant is zero then there are no imaginary solutions?
Yes, if the discriminant is zero, then there will be a double root, which will be real.Also, If the discriminant is positive, there will be two distinct real solutions. But if the discriminant is negative, then you will have two complex solutions.
How many real solutions does the following quadratic equation have by using the discriminant?
If the discriminant > 0 then 2 distinct real solutions.If the discriminant = 0 then 1 double real solution.If the discriminant < 0 then no real solutions (though there are two complex solutions).
How do you know if a quadratic equation will have more than one solutions?
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).
Can two parabolas of the form with different vertices have the same axis of symmetry?
The form is not specified in the question so it is hard to tell. But two parabolas with different vertices can certainly have the same axis of symmetry.
How many distinct factors does 45 have?
Six distinct factors Two distinct prime factors
Does every quadratic equation have two distinct real numbers in its solution set?
Nope. Consider x2+0x+1=0. This means x2+1=0. This has two solutions, but they are complex numbers: +i and -i, where i is the squareroot of -1. How about x2+0x+0=0? This means x2=0. This has two solutions, sure, but they aren't distinct. In this case, x=0 for both solutions, so we just consider them one solution.
Discriminant is negative how many solutions?
Two complex solutions.
What are the types of parabolas?
There are two ways of classifying parabolas: By the direction in which they are open: open at the top or at the bottom. By the number of real roots: 2 real, 1 real or no real roots.
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).
How many solutions does linear equation in two variable have?
A single linear equation in two variables has infinitely many solutions. Two linear equations in two variables will usually have a single solution - but it is also possible that they have no solution, or infinitely many solutions.
