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One of the five quadratics below has a repeated root. (The other four have distinct roots.) What is the repeated root?
\(\begin{align*} &-x^2 + 18x + 81 \\ &3x^2 - 6x + 9 \\ &8x^2 - 32x + 32 \\ &25x^2 - 30x - 9 \\ &x^2 - 14x + 196 \end{align*}\)

 May 17, 2022
 #1
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For a quadratic to have distinct roots, it's must be the form: \(a^2x^2 \pm 2abx + b^2\)

 

For example, applying this to the fifth one yields: \(1^2 x^2 - 2 \times 1 \times 14x + 14^2\), which equals: \(x^2- 28x+196\), this, isn't true, so it isn't 5. 

 

Can you do the rest?

 May 17, 2022
 #2
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Thank you for the help! It helps me learn a lot better when people don't give direct answers, but hints and help. Thank you!

Guest May 17, 2022
 #3
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That is really good to here.  Thanks  laugh

And thanks for your teaching style answer Builderboi.  laugh

 

If you become a member you will get known (positively I think) and then you will get a consistently good response (like this one)  from answerers here.  wink

Melody  May 17, 2022
 #4
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Okay, I will look into making an account :)

Guest May 17, 2022
 #5
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Guest: I'm so glad I could help!

 

Melody: Thank you!

 

Also, I just realized my original answer has a typo, it should be "For a quadratic to have repeated roots", not "For a quadratic to have distinct roots"

BuilderBoi  May 17, 2022
edited by BuilderBoi  May 17, 2022

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