This week in Precalculus 11 we learned about discriminant. A discriminant is a part of the quadratic equation that helps us determine many things such as if the equation is factorable, how many roots it has, or if it has any roots at all before we actually solve the whole thing.

Example

Equation:

3x^2 - 18x +27 = 0

Step 1: make sure to take out anything common

3(x^2 - 6 + 9)=0

Step 2: determine what a, b, and c are.

a = 1

b = -6

c  = 9

Step 3: fill the formula

(-6)^2 - 4(1)(9)

Step 4: simplify

(-6)^2 - 4(1)(9)

(36) – (36)

0

Explanation

Step 1: make sure to take out anything common

Taking out things that are common makes figuring out the answer a lot easier because the numbers are smaller to work with, but even if you leave everything in, it comes out with the same answer.

Step 2: determine what a, b, and c are

The formula for finding the discriminant relies on a, b, and c, and they are all in coordination with the equation. a would be equal to the first number (the number that has x^2 attached to it. b would be equal to the middle number (the number attached to x). c would be equal to the last number (the number that has no variable attached to it.). Writing out what a, b, and c are equal to makes it a less chance of error.

Step 3: fill the formula

Next, fill the formula according to coordination between letter and number

Step 4: simplify

There’s not much left to do except to find out the answer. The answer for this example was 0. This indicates that this equation has one real root. If the answer was any number bigger than 0 then that would mean that this equation has 2 real roots. If the answer was a number smaller than 0 (any negative number) then the equation has no real roots which means there is no need to solve the rest of the quadratic equation. That’s why it is helpful to find the discriminant, because we don’t need to solve more than we need to if we don’t need to.