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# If m is a real number and 2x^2+mx+6 has two distinct real roots

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If m is a real number and 2x^2+mx+6 has two distinct real roots, then what are the possible values of m? Express your answer in interval notation. Thanks

Oct 12, 2020

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What determines how many roots an equation has?

Its the... DISCRIMINANT, also known as b^2-4ac!

If the discriminant < 0, there are no real solutions. If the discriminant = 0, there is 1 real solution! However, if it is >0, there are two real solutions, as desired! Therefore, we have a=2 and c=6, so b^2-48>0, or b^2>48, so $b>\sqrt{48}.$

Oct 12, 2020