14 and 17 | Mathematics | Page 1

wraith vine Oct 15, 2023, 1:51 AM

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untold lanceBOT Oct 15, 2023, 1:51 AM

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wraith vine

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stone vector Oct 15, 2023, 1:54 AM

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wraith vine

Intersection means that f(x) - g(x) = 0, ie f(x) = g(x)

Let h(x) = f(x) - g(x). What is h(x)
Solve h(x) = 0 (quadratic formula)
What is discriminant (stuff inside sqrt)
For a quadratic to have one root, discriminant = 0. What value of k allows that

wraith vine Oct 15, 2023, 1:55 AM

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stone vector Intersection means that f(x) - g(x) = 0, ie f(x) = g(x) - Let h(x) = f(x) - g(x)...

what question r we doing

stone vector Oct 15, 2023, 1:55 AM

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wraith vine what question r we doing

14

wraith vine Oct 15, 2023, 1:55 AM

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k

stone vector Oct 15, 2023, 1:55 AM

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For 17 you do a very similar method

wraith vine Oct 15, 2023, 1:55 AM

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lets do 14 first

wraith vine Oct 15, 2023, 1:57 AM

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stone vector For 17 you do a very similar method

how do i do h(x)=0

stone vector Oct 15, 2023, 1:57 AM

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wraith vine how do i do h(x)=0

Do you have the equation for h(x)

wraith vine Oct 15, 2023, 1:57 AM

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yea

stone vector Oct 15, 2023, 1:58 AM

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Do you know quadratic formula

wraith vine Oct 15, 2023, 1:58 AM

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yea

stone vector Oct 15, 2023, 1:58 AM

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So what will the a,b, and c be for h(x)

wraith vine Oct 15, 2023, 1:58 AM

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stone vector So what will the a,b, and c be for h(x)

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is it this

stone vector Oct 15, 2023, 1:59 AM

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Yep

wraith vine Oct 15, 2023, 1:59 AM

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yay

stone vector Oct 15, 2023, 1:59 AM

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Now plug that into the quadratic formula

wraith vine Oct 15, 2023, 1:59 AM

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bet

wraith vine Oct 15, 2023, 2:05 AM

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stone vector Now plug that into the quadratic formula

now what

stone vector Oct 15, 2023, 2:05 AM

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wraith vine now what

So a quadratic only has one root if the stuff inside the square root equals zero

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What value of k will make that happen

wraith vine Oct 15, 2023, 2:05 AM

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84/8

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i think

stone vector Oct 15, 2023, 2:06 AM

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Correct

wraith vine Oct 15, 2023, 2:06 AM

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which is 21/2

stone vector Oct 15, 2023, 2:06 AM

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Yep

wraith vine Oct 15, 2023, 2:07 AM

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i got -7/4

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for x

wraith vine Oct 15, 2023, 2:11 AM

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stone vector Yep

what do i do now

stone vector Oct 15, 2023, 2:11 AM

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wraith vine what do i do now

You found the value of k, so the problem’s solved

wraith vine Oct 15, 2023, 2:12 AM

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stone vector You found the value of k, so the problem’s solved

but the answer sheet says the answer is 10.5

stone vector Oct 15, 2023, 2:12 AM

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wraith vine but the answer sheet says the answer is 10.5

Yea 21/2 = 10.5

wraith vine Oct 15, 2023, 2:12 AM

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oh

stone vector Oct 15, 2023, 2:12 AM

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You just had it in fraction form

wraith vine Oct 15, 2023, 2:12 AM

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okay i forgot about that

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now 17

stone vector Oct 15, 2023, 2:15 AM

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Again subtract the right hand side to get a quadratic equal to 0

wraith vine Oct 15, 2023, 2:16 AM

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done

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could i have cancelled out the (x-1)

stone vector Oct 15, 2023, 2:17 AM

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wraith vine could i have cancelled out the (x-1)

As long as x ≠ 1

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Tho for this problem I’d just leave it in

wraith vine Oct 15, 2023, 2:19 AM

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okay

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now what do i do

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if i cant subtract the (x-1)

stone vector Oct 15, 2023, 2:20 AM

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Expand out the quadratic

wraith vine Oct 15, 2023, 2:21 AM

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wraith vine Oct 15, 2023, 2:23 AM

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stone vector Expand out the quadratic

done

stone vector Oct 15, 2023, 2:23 AM

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wraith vine done

Now use quadratic formula (group together x^2,x and constant)

wraith vine Oct 15, 2023, 2:24 AM

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okay

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whats a constant

stone vector Oct 15, 2023, 2:24 AM

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wraith vine whats a constant

A term not affected by variable

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Like in 5x + 3, 3 is a constant cuz the value of “3” doesn’t change with x

wraith vine Oct 15, 2023, 2:25 AM

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alr

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wraith vine Oct 15, 2023, 2:28 AM

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stone vector Now use quadratic formula (group together x^2,x and constant)

now what?

stone vector Oct 15, 2023, 2:28 AM

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wraith vine now what?

Quadratic formula

wraith vine Oct 15, 2023, 2:29 AM

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how

stone vector Oct 15, 2023, 2:29 AM

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wraith vine how

So you have (k-1)x^2 + 2x + (-k + 1) = 0

wraith vine Oct 15, 2023, 2:30 AM

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what would a b and c be

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theres like more than three terms

stone vector Oct 15, 2023, 2:31 AM

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wraith vine theres like more than three terms

Look at my writing of the equation

wraith vine Oct 15, 2023, 2:32 AM

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a=k-1 b=2 c=k-1

stone vector Oct 15, 2023, 2:32 AM

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wraith vine a=k-1 b=2 c=k-1

Yep

wraith vine Oct 15, 2023, 2:32 AM

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alr one min

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i got k=0

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and x=-1

stone vector Oct 15, 2023, 2:35 AM

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wraith vine i got k=0

Show work

wraith vine Oct 15, 2023, 2:35 AM

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i got the right answer

stone vector Oct 15, 2023, 2:52 AM

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wraith vine a=k-1 b=2 c=k-1

Oh wait mb c is 1-k, not k-1

wraith vine Oct 15, 2023, 2:53 AM

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stone vector Oh wait mb c is 1-k, not k-1

i got the right answer so its fine

stone vector Oct 15, 2023, 2:54 AM

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wraith vine i got the right answer so its fine

No as for any value of k, there would only be one solution

wraith vine Oct 15, 2023, 2:55 AM

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okay

stone vector Oct 15, 2023, 2:58 AM

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Redo the quadratic with the fixed version of c

wraith vine Oct 15, 2023, 4:02 AM

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+closr

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+close

#14 and 17