In this episode of Engineer In Training Exam TV, Justin walks you through a Fundamentals of Engineering Exam Review of Quadratic Equations.

He will start by defining the standard form of the quadratic equation and run through a common way people go about solving such equations and follow it up with a way to simplify our work in complicated situations.

We will wrap this tutorial up with introducing the Discriminant and what it can tell us when using the quadratic equation.

This Fundamentals of Engineering Exam Review of Quadratic Equations is part of the global subject Mathematics.

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Hey what’s going on everyone, it’s Justin Dickmeyer from EngineerInTrainingExam.com.

In today’s video we are going to present a Fundamentals of Engineering Exam Review of Quadratic Equations.

We’ll start off this tutorial by defining a quadratic equation, we’ll move on to solving quadratic equations using factoring, then we’ll move on to the quadratic formula and finish off with defining the discriminant.

So let’s start off our Fundamentals of Engineering Exam Review of Quadratic Equations by defining exactly what a Quadratic Equation is.

So what is a Quadratic equation?

in its simplest form a

quadratic equation is ax squared plus BX

plus C is equal to 0 where a cannot

equal 0 so in other terms a quadratic

equation must have squared term as its

highest power so how do we solve

quadratic equations there are 4 methods

of solving these equations 1 we can

factor 2 completing the square factor by

grouping or using the quadratic formula

in this tutorial in this quick review

we’re going to talk about factoring and

the quadratic formula so a quadratic

equation can be solved by factoring if

after writing that equation in its

standard form the quadratic expression

factors completing this process can be

done in four steps step number one is

getting an equation we want to simplify

it we want to take away any parenthesis

division we want to add like terms

once simplified we want to get it that

equation into the standard form of ax

squared plus BX plus C is equal to 0

step number 3 factor

once we have factored we want to solve

so that’s all let’s look at a quick

example let’s take the equation x

squared plus 3x minus 10 is equal to 0

so the first step is to simplify that’s

completed step number two we want to get

in its standard form

once again convenient it’s completed

step number three we want to factor so

in this case this equation factors out

2x plus five multiplied by X minus 2 is

equal to 0 so we want this product to

equal to 0 so in step number four we

need to solve that and we can just

visualize and see that we’re going to

get X is equal to negative 5 and X is

equal to 2 so this quadratic quadratic

equation has two solutions X equal

negative 5 and X equal 2 so let’s talk

about the quadratic formula you can

solve any quadratic equation by using

the quadratic formula this is convenient

when a quadratic equation does not

factor or is difficult to factor so once

again there’s 4 steps or excuse me

there’s 5 steps in completing this

process step number one is given an

equation we want to simplify just like

that previous factoring we want to get

rid of any parenthesis division we want

to get rid of or combine like terms

step number two is the same as well we

want to get it into standard form so

once it’s in standard form of ax squared

plus BX plus C is equal to zero we can

move on to step number three which is we

need to identify what a is equal what B

is equal and what C is equal once we

identify what a B and C is we can take

the

podriatic formula which is X is equal to

negative b plus or minus the square root

of b squared minus 4ac divided by 2a so

we just take our values of a B and C and

we plug them into this equation and then

step number five would be whatever those

values all are if we can simplify and

make them complete whole numbers and

that’s great let’s do that so once again

let’s look at a quick example let’s take

the equation 2x squared minus 5x plus 1

is equal to zero

once again step number one of

simplifying is done step number two of

getting it in its standard form is

completed step number three in this case

a is equal to 2 B is equal to negative

five and C is equal to one step number

four we take the quadratic formula and

populate it so in this instance where

you go – of negative 5 plus or minus the

square root of negative five squared

minus four times two times one and

that’s all over two times two so let’s

move up here now that we have all of our

values for a B and C plugged into the

quadratic formula we can solve and we

get X is equal to 5 plus or minus the

square root of 25 minus eight divided by

four and this doesn’t simplify and do

whole numbers or anything but we can

simplify it a little bit as X is equal

to 5 plus or minus the square root of 17

divided by 4 so those are our two

solutions for this quadratic equation

so let’s talk about the discriminant

when we’re given an equation or a

quadratic equation x squared once again

BX plus C is equal to zero right off the

bat we can take a look at it and know if

we can divide define a B and C we can

define the discriminant and if we can

define the discriminant then we can use

a couple known factors to determine what

our solutions are going to look like to

these this equation so in other words

let me define it like this the

discriminant in the quadratic formula is

that under the square root of the

quadratic formula on the top which is b

squared minus 4ac so we have all these

defined in a given quadratic equation

and if we do we can determine what type

of solutions we should expect to see so

in other words we can put this into a

table say we define our discriminant and

that discriminant is less than 0 if it’s

less than zero then there are going to

be two distinct real number answers

solutions to that quadratic equation if

that discriminant is equal to zero then

there’s going to be one real number

solution if that discriminant is greater

than zero then there’s going to be two

distinct complex

imaginary numbers solutions so that’s it

so the discriminant once again the

quadratic equation minus B plus or minus

the square root of b squared minus 4ac

divided by 2a this right here that’s the

discriminant so once we get a quadratic

equation we can determine what the value

is of that discriminant take it to our

table and know what we know what to

expect when we determine our solutions

so that’s that that’s that quick

overview of quadratic equations I

appreciate you guys checking out the

YouTube channel don’t forget to head

back over to engineering training exam

comm and check out more free resources

for you as you prepare for the engineer

and training exam so good luck everybody

we’ll be talking soon.

—

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