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Math Challenge Three: 3.21 Algebra

 
 
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Re: Math Challenge Three: 3.21 Algebra
WangDr. Kevin - 2020年09月27日 Sunday 00:21
 

Here is the question:

Assume that $m$ and $n$ are real numbers and the quadratic equation (in $x$) $x^2 + 2(m+1)x + (3m^2+4mn+4n^2+2) = 0$ has real roots. Evaluate $3m^2+2n^2$.


If a quadratic equation has real roots, its discriminant is greater than or equal to $0$. From there you can have an inequality about $m$ and $n$. Then, try to complete the squares and see what happens.

 
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