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Heart of Algebra Videos 10 videos

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PSAT 1.14 Math Diagnostic 181 Views


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Description:

PSAT 1.14 Math Diagnostic. What value of b will make x have an imaginary component?


Transcript

00:00

Sorry And here's your shmoop du jour brought to you

00:05

by the square root sign Not surprisingly it's parents are

00:09

check mark and a horizontal line We're sure you can

00:11

see the resemblance All right if to x squared minus

00:15

b x equals negative nine what value of b will

00:18

make x have an imaginary component And here the pencil

00:23

and imaginary well you may want to bring your imaginary

00:27

friend along for this one after all he's got credit

00:30

Okay We'll need to borrow the quadratic formula to solve

00:33

this baby So best to start by rearranging the equation

00:37

were given so it you know has that love and

00:40

feeling well that quadratic no way So we're going to

00:44

take to x squared minus b x equals negative nine

00:47

and add nine to both sides to get to x

00:49

squared minus b x plus nine equals zero they're quadratic

00:55

enough for you Okay now we need to find a

00:58

value for p when Acts as a non 0 imaginary

01:01

heart so let's use the discriminated shortcut he all that

01:05

good stuff under the square root sign in the quadratic

01:08

formula there b squared minus four a c ever plug

01:12

in a value for be here and you wind up

01:14

with a negative number Well then x has a non

01:17

zero imaginary part On the flip side of that coin

01:20

of your results is greater than or equal to zero

01:23

and the solution won't have an imaginary part Got it

01:26

It will be really sometimes to really plugging chuck time

01:30

The coefficient of our x squared term is to and

01:33

our last term is positive Nine so we get b

01:37

squared minus four times two times nine We'll set that

01:40

equal to zero four times two times nine is seventy

01:43

two so this simplifies to be squared minus seventy two

01:47

And then we add something to both sides Get b

01:49

squared equals seventy two and finally take the square root

01:53

of both sides Get that b is greater than or

01:55

equal to six square root of two Okay deep breath

02:01

Now as long as b is greater than or equal

02:04

to six square root of two x won't have an

02:07

imaginary heart However we're looking for the value that will

02:11

make x have an imaginary part And the only answer

02:15

choice that is smaller than six square root of two

02:17

is option A Where were the three but that's Our

02:20

answer course We believe that imaginary numbers should have all

02:23

the same rights and privileges as real numbers way Dont 00:02:26.99 --> [endTime] want to discriminate

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