Contents

- 1 What discriminant means?
- 2 How do you find the discriminant?
- 3 How do you use the discriminant to find roots?
- 4 Why do we use the discriminant?
- 5 What does a discriminant of 1 mean?
- 6 What happens when B 2 4ac 0?
- 7 How do you tell if the discriminant is positive on a graph?
- 8 What number and type of roots are associated with a discriminant of?
- 9 Are there two distinct real roots?
- 10 What are real roots in quadratic equation?
- 11 What happens when the discriminant is a perfect square?
- 12 Why is it called the discriminant?
- 13 How many roots are there if the discriminant is negative?

## What discriminant means?

The discriminant is the term underneath the square root in the quadratic formula and tells us the number of solutions to a quadratic equation. If the discriminant is positive, we know that we have 2 solutions. If it is negative, there are no solutions and if the discriminant is equal to zero, we have one solution.

## How do you find the discriminant?

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 use the discriminant to find roots?

Correct answer: b^{2} – 4ac = (8)^{2} – 4(1)(16) = 64 – 64 = 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.

## 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 does a discriminant of 1 mean?

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.

## 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.

## 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 number and type of roots are associated with a discriminant of?

The expression under the square root, b2−4ac, is called the discriminant. Can you make a conjecture about the relationship between the discriminant and the roots of quadratic equations? Investigating the nature of roots.

rational | unequal | real |
---|---|---|

perfect square | irrational | undefined |

## Are there two distinct real roots?

For the quadratic equation ax2 + bx + c = 0, the expression b2 – 4ac is called the discriminant. The value of the discriminant shows how many roots f(x) has: – If b2 – 4ac > 0 then the quadratic function has two distinct real roots. – If b2 – 4ac < 0 then the quadratic function has no real roots.

## What are real roots in quadratic equation?

For an equation ax^{2}+bx+c = 0, b^{2}-4ac is called the discriminant and helps in determining the nature of the roots of a quadratic equation. If b^{2}-4ac > 0, the roots are real and distinct. If b^{2}-4ac = 0, the roots are real and equal. If b^{2}-4ac < 0, the roots are not real (they are complex).

## 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.

## 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)

## How many roots are there if the discriminant is negative?

That’s negative, so there are two complex roots for this equation.