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A positive discriminant means the quadratic equation will have how many solutions?
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What type of equation is b2-4ac?
6
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).
When the discriminant is positive the answer to the quadratic equation will be?
Then x will have two different distinct roots
How many solutions are there if the discriminant of the equation is positive?
There are two distinct real solutions.
How does the discriminant affect the roots of a quadratic equation?
If the discriminant is negative, the roots will be two unreal complex conjugates. If the discriminate is positive the roots will be real.
What type of equation is b2-4ac?
6
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).
What is the type of the solution determined by?
It depends on the discriminant value of the quadratic equation. If the discriminant is positive, there are two distinct real solutions; if it is zero, there is one real solution; and if it is negative, there are two complex conjugate solutions.
If the discriminant is positive how many solutions does the equation have?
2
What does the discriminant tell you?
The discriminant tells you how many solutions there are to an equation The discriminant is b2-4ac For example, two solutions for a equation would mean the discriminant is positive. If it had 1 solution would mean the discriminant is zero If it had no solutions would mean that the discriminant is negative
When the discriminant is positive the answer to the quadratic equation will be?
Then x will have two different distinct roots
How many solutions are there if the discriminant of the equation is positive?
There are two distinct real solutions.
What is the expression b2-4ac under the radical sign in the quadratic formula?
6
What is true about a quadratic equation when the discriminant of the equation is positive?
It will then have 2 different roots If the discriminant is zero than it will have have 2 equal roots
How do you know if a quadratic equation can be factored?
The answer depends on what the factors will be. For example, every quadratic can be factored if you allow complex numbers. If not, then it helps to use the discriminant. If it is positive, there are two real factors or solutions. If that positive number is a perfect square, then the factors are rational numbers. If not, they are real but not rational (irrational). If the discriminant is 0, there is one real solution. Lastly, if it is negative, there are no real solutions.
How does the discriminant affect the roots of a quadratic equation?
If the discriminant is negative, the roots will be two unreal complex conjugates. If the discriminate is positive the roots will be real.
If the discriminant is negative the equation has solutions?
As stated in the attached link, there are three possible discriminant conditions: Positive, Zero, or Negative. If the discriminant is negative, there are no real solutions but there are two imaginary solutions. So, yes there are solutions if the discriminant is negative. The solutions are imaginary, which is perfectly acceptable as solutions.
