a: \(\text{Δ}=\left[-\left(m+5\right)\right]^2-4\left(2m+6\right)\)
\(=m^2+10m+25-8m-24\)
\(=m^2+2m+1=\left(m+1\right)^2>=0\forall m\)
=>Phương trình luôn có hai nghiệm
b: Theo Vi-et, ta có:
\(\left\{{}\begin{matrix}x_1+x_2=-\dfrac{b}{a}=m+5\\x_1x_2=\dfrac{c}{a}=2m+6\end{matrix}\right.\)
\(x_1^2+x_2^2=35\)
=>\(\left(x_1+x_2\right)^2-2x_1x_2=35\)
=>\(\left(m+5\right)^2-2\left(2m+6\right)=35\)
=>\(m^2+10m+25-4m-12-35=0\)
=>\(m^2+6m-22=0\)
=>\(m=-3\pm\sqrt{31}\)
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