what is ment by the "discriminant"

The discriminant is b^2-4ac, or the part behind the square root in the quadratic formula. Try this website for more info.

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Without the spaces, of course.

When:

y=a*x^2+b*x+c

Then Discriminant is:

Ä=b^2-4*a*c

Go to en.wikipedia organd type "Dioscriminant"

The discriminant is a mathematical term commonly used in algebra and calculus. It is derived from the quadratic equation and provides information about the nature and number of solutions for a quadratic equation.

To understand the discriminant, we need to start with the standard form of a quadratic equation: ax^2 + bx + c = 0. The discriminant is represented by the expression b^2 - 4ac, where b, a, and c are coefficients of the equation.

Now, to compute the discriminant, you can follow these steps:

1. Identify the coefficients a, b, and c from the quadratic equation.
2. Square the value of coefficient b.
3. Multiply the coefficients a and c.
4. Subtract the result obtained in step 3 from the result obtained in step 2.

Once you have calculated the discriminant, it can be categorized into three possible scenarios:

1. If the discriminant is greater than 0 (D > 0), then the quadratic equation has two distinct real solutions. This means that the equation crosses the x-axis at two distinct points.
2. If the discriminant is equal to 0 (D = 0), then the quadratic equation has a single real solution. This means that the equation touches the x-axis at one point (also known as a "double root").
3. If the discriminant is less than 0 (D < 0), then the quadratic equation has no real solutions. This means that the equation does not intersect or touch the x-axis at any real point. Instead, it has two complex conjugate solutions, involving imaginary numbers.

In summary, the discriminant is a mathematical tool used to determine the number and nature of solutions for a quadratic equation. By calculating the discriminant, you can determine whether the equation has real solutions or complex ones.