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 are examples of quadratic polynomials?

Quadratic Polynomial Formula Example Here, the values of x =1 and x = 2 satisfy the equation x² – 3x + 2 = 0. These are known as solutions or roots of the quadratic equation. It also implies that numbers 1 and 2 are the zeros of the polynomial x² – 3x + 2.

#### What does factoring a quadratic mean?

Often the easiest method of solving a quadratic equation is factoring. Factoring means finding expressions that can be multiplied together to give the expression on one side of the equation. If a quadratic equation can be factored, it is written as a product of linear terms.

What does it mean if the discriminant is 0?

What is the discriminant? 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 if the discriminant is less than zero?

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.

## Why called the method solving quadratic equations by factoring?

To solve quadratics by factoring, we use something called “the Zero-Product Property”. Therefore, when solving quadratic equations by factoring, we must always have the equation in the form “(quadratic expression) equals (zero)” before we make any attempt to solve the quadratic equation by factoring.

### Why do we factor quadratic equations?

Explanation: Because it tells you what the roots of the equation are, i.e. where ax2+bx+c=0 , which is often a useful thing to know. This is a factored quadratic equation.

#### How can you tell if a graph is quadratic?

There is an easy way to tell whether the graph of a quadratic function opens upward or downward: if the leading coefficient is greater than zero, the parabola opens upward, and if the leading coefficient is less than zero, the parabola opens downward.

For the Quadratic Formula to work, you must have your equation arranged in the form ” (quadratic) = 0 “. Also, the ” 2a ” in the denominator of the Formula is underneath everything above, not just the square root.

When is a quadratic form a positive semideﬁnite?

A quadratic form is positive semideﬁnite if and only if all principal minors are ‚ 0; 2. A quadratic form is negative semideﬁnite if and only if all principal minors of odd degree are • 0, and all principal minors of even degree are ‚ 0.

## When is a quadratic form called a nondegenerate form?

If none of the terms are 0, then the form is called nondegenerate; this includes positive definite, negative definite, and indefinite (a mix of 1 and −1); equivalently, a nondegenerate quadratic form is one whose associated symmetric form is a nondegenerate bilinear form.

### When did Brahmagupta write the quadratic formula?

The Indian mathematician Brahmagupta (597–668 AD) explicitly described the quadratic formula in his treatise Brāhmasphuṭasiddhānta published in 628 AD, but written in words instead of symbols.