What does it mean if the discriminant is greater than 0?
When the discriminant is greater than 0, there are two distinct real roots. When the discriminant is equal to 0, there is exactly one real root. When the discriminant is less than zero, there are no real roots, but there are exactly two distinct imaginary roots. In this case, we have two real roots.
What happens when the discriminant is positive?
A positive discriminant indicates that the quadratic has two distinct real number solutions. A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.
How many real solutions if the discriminant is greater than zero?
If the discriminant is greater than zero, there are two solutions. If the discriminant is less than zero, there are no solutions and if the discriminant is equal to zero, there is one solution.
What does it mean if the discriminant is less than 0?
If the discriminant of a quadratic function is less than zero, that function has no real roots, and the parabola it represents does not intersect the x-axis.
When the discriminant is greater than zero but not a perfect square then the roots are?
When a, b, and c are real numbers, a ≠ 0 and the discriminant is a perfect square but any one of a or b is irrational then the roots of the quadratic equation ax2 + bx + c = 0 are irrational….Nature Of Roots.
| b2 – 4ac > 0 | Real and unequal |
|---|---|
| b2 – 4ac > 0 (is not a perfect square) | Real, irrational and unequal |
What is a discriminant example?
Example: Find the discriminant of the quadratic equation 2×2 – 3x + 8 = 0. Comparing the equation with ax2 + bx + c = 0, we get a = 2, b = -3, and c = 8. So the discriminant is, Δ OR D = b2 − 4ac = (-3)2 – 4(2)(8) = 9 – 64 = -55.
What is the discriminant of 76?
The discriminant is 76, which is positive. This means that there are two real solutions.
What is discriminant value?
discriminant, in mathematics, a parameter of an object or system calculated as an aid to its classification or solution. In the case of a quadratic equation ax2 + bx + c = 0, the discriminant is b2 − 4ac; for a cubic equation x3 + ax2 + bx + c = 0, the discriminant is a2b2 + 18abc − 4b3 − 4a3c − 27c2.
What does it mean when a discriminant is more than 0?
If a discriminant is more than or equal to 0, what does it mean? What about when a discriminant is less than or equal to 0? If the discriminant of quadratic equation is positive then the roots are real and they exist. If the discriminant of quadratic equation is equal to zero then the roots are real and they are equal.
What are the roots if the discriminant is zero?
When a, b, and c are real numbers, a ≠ 0 and the discriminant is zero, then the roots α and β of the quadratic equation ax2+ bx + c = 0 are real and equal. Considering this, how many solutions are there if the discriminant is zero?
What does a positive discriminant mean in math?
The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation. A positive discriminant indicates that the quadratic has two distinct real number solutions.
What are the characteristics of discriminant algebra?
The formula of discriminant algebra exhibits the following characteristics – When discriminant is zero, it shows that there are repeated real number solution to the quadratic; For a negative discriminant, neither of the solutions amount to real numbers;