Contents

- 1 What does discriminant mean?
- 2 How do you find the discriminant?
- 3 Why is it called the discriminant?
- 4 Why do we use the discriminant?
- 5 What happens when the discriminant is a perfect square?
- 6 How do you tell if the discriminant is positive on a graph?
- 7 What happens when B 2 4ac 0?
- 8 Is called the discriminant?
- 9 How do you tell if a quadratic has no solution?
- 10 How many real solutions are there if the value of k 0?
- 11 How many solutions are there if the discriminant is 0?
- 12 How do you show that the roots of an equation are real?
- 13 Who invented discriminant?

## What does discriminant mean?

The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.

## How do you find the discriminant?

The discriminant is the part under the square root in the quadratic formula, b²-4ac. If it is more than 0, the equation has two real solutions. If it’s less than 0, there are no real solutions. If it’s equal to 0, there is one real solution.

## Why is it called the discriminant?

It is called the Discriminant, because it can “discriminate” between the possible types of answer: when b^{2} − 4ac is positive, we get two Real solutions. when it is zero we get just ONE real solution (both answers are the same)

## Why do we use the discriminant?

The quadratic equation discriminant is important because it tells us the number and type of solutions. This information is helpful because it serves as a double check when solving quadratic equations by any of the four methods (factoring, completing the square, using square roots, and using the quadratic formula).

## What happens when the discriminant is a perfect square?

If the discriminant is a perfect square, then the solutions to the equation are not only real, but also rational. If the discriminant is positive but not a perfect square, then the solutions to the equation are real but irrational.

## How do you tell if the discriminant is positive on a graph?

Remember, the solutions to a quadratic equation are often called roots or zeros. The roots/zeros/solutions are the the values for x that make the equation equal to 0. On a graph, this will be where the parabola crosses the x-axis. Anytime the discriminant is positive, the graph will cross the x-axis twice.

## What happens when B 2 4ac 0?

1. b^{2} − 4ac < 0 There are no real roots. 2. b^{2} − 4ac = 0 There is one real root.

## Is called the discriminant?

The argument (that is, the contents) of the square root, being the expression b^{2} – 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 do you tell if a quadratic has no solution?

In the quadratic formula, if the discriminant is greater than or equal to 0, then the solutions to the quadratic equation will be real numbers. If the discriminant is less than 0, the equation has no real solution.

## How many real solutions are there if the value of k 0?

( If k = 0, there is only one distinct solution, sometimes called a double solution.)

## How many solutions are there if the discriminant is 0?

It tells you the number of solutions to a quadratic equation. 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.

## How do you show that the roots of an equation are real?

The discriminant (EMBFQ)

- If Δ<0, then roots are imaginary (non- real ) and beyond the scope of this book.
- If Δ≥0, the expression under the square root is non-negative and therefore roots are real.
- If Δ=0, the roots are equal and we can say that there is only one root.

## Who invented discriminant?

The term ” discriminant ” was coined in 1851 by the British mathematician James Joseph Sylvester.