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# HELP FAST

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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
+2

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
+117494
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That is really good to here.  Thanks

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.

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