ShmoopTube

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

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

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

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see the resemblance All right if to x squared minus

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b x equals negative nine what value of b will

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make x have an imaginary component And here the pencil

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and imaginary well you may want to bring your imaginary

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

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

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this baby So best to start by rearranging the equation

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were given so it you know has that love and

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

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take to x squared minus b x equals negative nine

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and add nine to both sides to get to x

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

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enough for you Okay now we need to find a

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value for p when Acts as a non 0 imaginary

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

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good stuff under the square root sign in the quadratic

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formula there b squared minus four a c ever plug

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in a value for be here and you wind up

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with a negative number Well then x has a non

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zero imaginary part On the flip side of that coin

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of your results is greater than or equal to zero

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

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It will be really sometimes to really plugging chuck time

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The coefficient of our x squared term is to and

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our last term is positive Nine so we get b

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

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equal to zero four times two times nine is seventy

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two so this simplifies to be squared minus seventy two

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And then we add something to both sides Get b

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squared equals seventy two and finally take the square root

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of both sides Get that b is greater than or

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equal to six square root of two Okay deep breath

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Now as long as b is greater than or equal

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

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

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make x have an imaginary part And the only answer

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choice that is smaller than six square root of two

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

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answer course We believe that imaginary numbers should have all

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

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