How do you solve a quadratic equation with no real solution?

How do you solve a quadratic equation with no real solution?

ax2 + bx + c = 0 There is a special case that will tell us if a quadratic has no real solution: if b = 0 when a and c share the same sign (both positive or both negative), then there will be no real solution. The quadratic formula becomes much simpler when b = 0.

Can a quadratic have 0 solutions?

As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b2 – 4ac), is positive, negative, or zero. This expression has a special name: the discriminant.

How do you write no real solutions in math?

Sometimes we use the symbol Ø to represent no solutions. That symbol means “empty set” which means that the set of all answers is empty. In other words, there is no answer. So if we want to use Ø to represent no solution, we may.

How do you change intercept form to vertex form?

Using the standard equation of y=ax^2+bx+c, find the x value of the vertex point by plugging the a and b coefficients into the formula x= -b/2a. Substitute the found value of x into the original equation to find the value of y. The values of x and y are the coordinates of the vertex.

How do you convert standard form to vertex form?

Changing from Standard Form to Vertex Form

1. Standard form of a Quadratic equation is written, ax^2 +bx +c = y.
2. Vertex form is written, a(x-h)^2 +k=y.
3. Step 1 .
4. Step 2 .Create a space between the second and third term.
5. Step 3 .Now complete the square, by taking the b term (second term) and half it and square it.

How do you find the real solution of a quadratic equation?

When The Coefficient of x2 Is Equal To 1 (a = 1) If this is true, then the quadratic has one solution, which is x = -b / 2. For example, the quadratic equation x2 + 8x + 16 has one solution.