Contents

- 1 How do you find the discriminant?
- 2 What discriminant means?
- 3 Why is it called the discriminant?
- 4 How do you use the discriminant to find roots?
- 5 Why is getting the discriminant important?
- 6 What does a discriminant of 1 mean?
- 7 What happens when B 2 4ac 0?
- 8 What does it mean if the discriminant is less than 0?
- 9 How do you know if a quadratic equation has no solution?
- 10 Is called the discriminant?
- 11 Are there two distinct real roots?
- 12 What are real roots in quadratic equation?
- 13 What number and type of roots are associated with a discriminant of?

## How do you find the discriminant?

The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac.

## 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.

## 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 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 is getting the discriminant important?

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?

If ( b^{2} – 4ac ) > 0.0, two real roots exist (i.e, the equation crosses the x-axis in two places — the x-intercepts). root of a negative number). If ( b^{2} – 4ac ) = 0, then only one real root exists — where the parabola touches the x-axis at a single point.

## 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.

## How do you know if a quadratic equation has no solution?

If the discriminant is less than 0, the equation has no real solution. Looking at the graph of a quadratic equation, if the parabola does not cross or intersect the x-axis, then the equation has no real solution. And no real solution does not mean that there is no solution, but that the solutions are not real numbers.

## 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.

## 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 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 |