Understanding Quadratic Equations - Algebra II

Make sure you keep track of negative signs when doing FOIL, especially when doing the Outer and Inner steps.

When the 2 terms differ only in their sign, the -term drops out from the final product.

In order to evaluate one needs to multiply the expression by itself using the laws of FOIL. In the foil method, one multiplies in the following order: first terms, outer terms, inner terms, and last terms.

Multiply terms by way of FOIL method.

Now multiply and simplify.

Use the FOIL method (First, Outer, Inner, Last):

Put all of these terms together:

Combine like terms:

The discriminant is found using the formula . In this case:

To find the discriminant, use the formula . In this case:

To determine the amount of roots a given quadratic function has, we must find the discriminant, which for

is equal to

If d is negative, then we have two roots that are complex conjugates of one another. If d is positive, than we have two real roots, and if d is equal to zero, then we have only one real root.

Using our function and the formula above, we get

Thus, the function has only one real root.

Identify the coefficients for the polynomial .

Write the expression for the discriminant. This is the expression inside the square root from the quadratic formula.

Substitute the numbers.

The answer is:

In general, the discriminant is .

In this particual case .

Plug in these three values and simplify:

Given the quadratic equation of

The formula for the discriminant is (remember this as a part of the quadratic formula?)

Plugging in values to the discriminant equation:

So the discriminant is 57. What does that mean for our solutions? Since it is a positive number, we know that we will have 2 real solutions. So the answer is:

57, 2 real solutions

The discriminant is found by using the formula . In this case:

For the equation

to have two imaginary solutions, its discriminant must be negative. Set and solve for in the inequality

Therefore, if is a positive integer, it must be in the set .

For the equation

to have two real solutions, its discriminant must be positive. Set and solve for in the inequality

Therefore, if is a positive integer, it must be in the set

Remember the quadratic formula:

.

The discriminant in the quadratic formula is the term that appears under the square root symbol. It tells us about the nature of the roots.

So, to find the discriminant, all we need to do is compute for our equation, where .

We get .

The "discriminant" is the name given to the expression that appears under the square root (radical) sign in the quadratic formula, where , , and are the numbers in the general form of a quadratic trinomial: . If the discriminant is positive, the equation has real roots, and if it is negative, we have imaginary roots. In this case, , , and , so the discriminant is , and because it is negative, this equation's roots are not real.

The discriminant is found using the equation . So for the function , ,, and . Therefore the equation becomes .

The number of roots can be found by looking at the discriminant. The discriminant is determined by . For this function, ,, and . Therfore, . When the discriminant is positive, there are two real solutions to the function.

Given that quadratics can be written as . The discriminant can be found by looking at or the value under the radical of the quadratic formula. Using substiution and order of operations we can find this value of the discriminant of this quadratic equation.

The discrimiant will determine how many solutions a quadratic has. If the discriminant is positive, then there are two real solutions. If it is negative then there are two immaginary solutions. If it is equal to zero then there is one repeated solution.

Given that quadratics can be written as . The discriminant can be found by looking at or the value under the radical of the quadratic formula. Using substiution and order of operations we can find this value of the discriminant of this quadratic equation.

The discriminant is positive; therefore, there are two real solutions to this quadratic.