What happens if the discriminant is negative?
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.
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.
What do you mean by discriminant?
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.
Why is it called discriminant?
The argument (that is, the contents) of the square root, being the expression b2 – 4ac, is called the “discriminant” because, by using its value, you can “discriminate” between (that is, be able to tell the difference between) the various solution types.
How many solutions if the discriminant is negative?
If the discriminant is positive, there are 2 real solutions. If it is 0 , there is 1 real repeated solution. If the discriminant is negative, there are 2 complex solutions (but no real solutions).
What is b2 4ac used for?
The expression b2 – 4ac from beneath the radical sign is called the discriminant, and it can actually determine for you how many solutions a given quadratic equation has, if you don’t feel like actually calculating them.
How many solutions are there if the discriminant is negative?
What is 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 another word for discriminant?
discriminative, discriminate, discriminatory.
What is a discriminant example?
Examples. In our example, our quadratic equation gives us 1 for our letter a, 5 for letter b, and 4 for letter c. We take these values and plug them into their appropriate places in the discriminant formula, and we’ll find that our discriminant equals 9, a positive number.