# What is the discriminant of the following quadratic equation

• Yichen
If so, your summary could be:"In summary, the given equation represents a quadratic equation with the unknown values of ||v|| and ||w||. It can be used to prove the Cauchy-Schwarz inequality by finding the solution where c = ||v||/||w||."
Yichen
• quadratic equation ||v||^2 - c(2v·w)+c^2||w||^2=0, where c belongs to any real number, v and w are both vectors

Hello Yichen,

Please post in the homework forum. There is a most useful template there for questions like this.
If this is an equation, what are the knowns and what is the unknown ?
I read your equation as equivalent to $$\left ({\bf \vec v} - c {\bf \vec w } \right ) \cdot \left ({\bf \vec v} - c {\bf \vec w } \right ) = 0$$ which certainly has a solution ##\ {\bf \vec v} = c {\bf \vec w } ##

Yichen said:
• quadratic equation ||v||^2 - c(2v·w)+c^2||w||^2=0, where c belongs to any real number, v and w are both vectors

Are you attempting to prove the Cauchy-Schwarz inequality?

## 1. What is the discriminant of a quadratic equation?

The discriminant of a quadratic equation is a term that is used to determine the nature of the solutions to the equation. It is calculated using the formula b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form of ax^2 + bx + c.

## 2. How is the discriminant used to determine the nature of the solutions?

If the discriminant is positive, the equation will have two distinct real solutions. If it is zero, the equation will have one real solution. And if the discriminant is negative, the equation will have two complex solutions.

## 3. Can the discriminant be used to solve a quadratic equation?

No, the discriminant only helps to determine the nature of the solutions, but it does not provide the actual solutions. To solve a quadratic equation, you would need to use other methods such as factoring, completing the square, or using the quadratic formula.

## 4. What does the discriminant tell us about the graph of a quadratic equation?

The discriminant can tell us the number of x-intercepts that the graph of a quadratic equation will have. If the discriminant is positive, the graph will intersect the x-axis at two distinct points. If it is zero, the graph will touch the x-axis at one point. And if the discriminant is negative, the graph will not intersect the x-axis at all.

## 5. How is the discriminant used in the quadratic formula?

The discriminant is used in the quadratic formula to determine the values of x that satisfy the equation. If the discriminant is positive, the formula will give two real solutions. If it is zero, there will be one real solution. And if the discriminant is negative, the formula will give two complex solutions.

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