0
Suppose the equation ax^2 + bx + c = 0 has the discriminant d.Then the solutions to the quadratic are:
x1 = [-b - sqrt(d)]/2a and x2 = [-b + sqrt(d)]/2a
If d > 0 then sqrt(d) is some real non-zero number.
Sqrt(d) is real implies x1 and x2 are real.
sqrt(d) is non-zero implies that x1 and x2 are distinct.
Add your answer:
Earn +20 pts
How many solutions will a problem have if the discriminant is positive?
Two real roots.
How many real solutions does a quadratic function have when the value of its discriminant is seven?
If the discriminant is positive, as in this case, there are two real solutions.Also: * If the discriminant is zero, there is one real solution, considered to be a "double solution" because of the way polynomials are factored. * If the discriminant is negative, there are two complex solutions, which are complex and non-real.
If the discriminant of a quadratic equation is -4 how many solutions does the equation have?
If the discriminant of a quadratic equation is less then 0 then it will have 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.
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).
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 solutions are there if the discriminant of the equation is positive?
There are two distinct real solutions.
How many solutions will a problem have if the discriminant is positive?
Two real roots.
How many real solutions does a quadratic function have when the value of its discriminant is seven?
If the discriminant is positive, as in this case, there are two real solutions.Also: * If the discriminant is zero, there is one real solution, considered to be a "double solution" because of the way polynomials are factored. * If the discriminant is negative, there are two complex solutions, which are complex and non-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.
A positive discriminant means the quadratic equation will have how many solutions?
Two distinct real solutions.
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.
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).
What kind of solution does an equation has if the discriminant is negative?
If the discriminant is negaitve, there are no "real" solutions. The solutions are "imaginary".
How can you have one solution in something that is quadratic?
b^2 - 4ac, the discriminant will tell you that a quadratic equation may have one real solution( discriminant = 0 ) , two real solutions( discriminant > 0 ), or no real solutions( discriminant < 0 ).
What is a discriminant and how does help to solve equations?
In the quadratic formula, the discriminant is b2-4ac. If the discriminant is positive, the equation has two real solutions. If it equals zero, the equation has one real solution. If the discriminant is negative, it has two imaginary solutions. This is because you find the square root of the discriminant and add or subtract it from -b and divide the sum or difference by 2a. If the square root is of a positive number, then you get two different solutions, one from adding the discriminant to -b and one from subtracting the discriminant from -b. If the square root is of zero, then it equals zero, and the solution is -b/2a. If the square root is of a negative number, then you have two imaginary solutions because you can't take the square root of a negative number and get a real number. One solution is from subtracting the discriminant from -b and dividing by 2a, and the other is from adding it to -b and dividing by 2a. The parabola on the left has a positive discriminant. The parabola in the middle has a discriminant of zero. The parabola on the right has a negative discriminant.
What type of equation is b2-4ac?
6
