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For what real value of v is \(\frac{-21-\sqrt{301}}{10}\) a root of \(5x^2+21x+v\)?

 Apr 17, 2020
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\(5x^2+21x+v\) \(=0\)

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

\(x = {-21 \pm \sqrt{21^2-20v} \over 10}\)

\( {-21 \pm \sqrt{21^2-20v} \over 10}= {-21 \pm \sqrt{301} \over 10}\)

\(\sqrt{21^2-20v}=\sqrt{301}\)

\(21^2-20v=301\)

\(301-21^2=-20v\)

\(v=\frac{-140}{-20}=7\)

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 Apr 17, 2020

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