# What if the discriminant is zero? –

## What if the discriminant is zero?

A discriminant of zero indicates that the quadratic has a repeated real solution. A negative discriminant indicates that none of the solutions are real numbers.

## What does it mean when the discriminant is less than 0?

When the discriminant is zero, the equation will have a unique solution (the equation is also said to have a double solution). If it is less than zero, since there are no roots of negative numbers, the equation will have no solutions.

How to know what is the value of the discriminant?

In mathematics, the discriminant of a quadratic equation of the form ax2+bx+c=0 is a number obtained from the coefficients of the equation. The discriminant of the equation ax2+bx+c=0 is equal to b2-4ac. The notation used for the discriminant is Δ (delta), so we have the formula Δ=b2-4ac.

What does it mean that the roots are imaginary?

Furthermore, we know that if the discriminant “b2 – 4ac ≥ 0” the solution is made up of real numbers. But when “b2 – 4ac < 0”, there is no solution in real numbers, but two solutions that include imaginary numbers and that satisfy the given equation.

### When the equation is equal to zero?

If ab = 0, then either a = 0 or b = 0, or both a and b are 0. This property may seem obvious, but it has big implications for solving quadratic equations. If we have a factored polynomial that is equal to 0, you know that at least one or both of the factors is 0.

### What happens when the discriminant of b2 − 4ac is less than zero?

if the discriminant is positive, b2 – 4ac > 0, there are TWO solutions. if it is zero, b2 – 4ac = 0, there is only ONE solution, if it is negative, b2 – 4ac < 0, there are TWO solutions that include imaginary numbers.

How are the roots of a Quadratic if the expression b2 4ac 0?

What we call the Discriminant of a polynomial – If Δ = b2 – 4ac > 0 then there are two distinct real roots. – If Δ = b2 – 4ac < 0 then there are no real roots (two conjugate imaginary roots). Example 1: Given the equation 2×2 –3x + k + 2 = 0, determine the value of k so that the roots (solutions) are equal.

What is the value of b2 4ac?

Where the expression “b2 – 4ac” (which is inside the quadratic root) is called the discriminant; its sign will determine the number of solutions of the quadratic equations and also whether these are real or imaginary solutions: if the discriminant is positive, b2 – 4ac > 0, there are TWO solutions.

## What figure represents a quadratic equation on the Cartesian plane?

The smooth curve is called a parabola and it is the image that is generated when the basic quadratic function is placed on a Cartesian grid. The green point is known as the vertex of the parabola. The parabola opens up because the \begin{align*}y\end{align*}values ​​from the table of values ​​are 0, 1, 4, and 9.

## How to know if the roots are real or imaginary?

What we call the Discriminant of a polynomial – If Δ = b2 – 4ac > 0 then there are two distinct real roots. – If Δ = b2 – 4ac = 0 then there is a double root (two equal real roots). – If Δ = b2 – 4ac < 0 then there are no real roots (two conjugate imaginary roots).

When does a parabola have imaginary roots?

When a quadratic function does not cut the x-axis, it has complex roots. Solving the roots of a function algebraically with the quadratic formula will leave a negative below the square root symbol.

What is the concept of discriminant?

The concept of discriminant has been generalized to other algebraic structures besides polynomials, including conic sections, quadratic forms, and algebraic number fields. Discriminants in algebraic number theory are closely related and contain information about branches.

### What is a positive discriminant?

The discriminant can be positive, zero or negative and this determines how many solutions (or roots) there are for the given quadratic equation. A positive discriminant indicates that the quadratic has two different real solutions.

### How is the discriminant removed?

In this case, the discriminant vanishes if and only if the polynomial has multiple roots in its decomposition field. The concept of discriminant has been generalized to other algebraic structures besides polynomials, including conic sections, quadratic forms, and algebraic number fields.

What is the solution of the discriminant?

If the discriminant is zero, there is only one solution. If the discriminant is positive, then the ± symbol means you get two responses. The solutions of this equation correspond to the x-intercepts of the parabola y = ax 2 + bx + c.