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# How do you do this???

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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