a: \(\text{Δ}=3^2-4\cdot1\cdot m=-4m+9\)
Để phương trình có nghiệm thì Δ>=0
=>-4m+9>=0
=>-4m>=-9
=>\(m< =\dfrac{9}{4}\)
b: Theo Vi-et, ta có:
\(\left\{{}\begin{matrix}x_1+x_2=-\dfrac{b}{a}=-3\\x_1x_2=\dfrac{c}{a}=m\end{matrix}\right.\)
\(x_1^2+x_2^2=34\)
=>\(\left(x_1+x_2\right)^2-2x_1x_2=34\)
=>\(\left(-3\right)^2-2m=34\)
=>2m=9-34=-25
=>m=-12,5(nhận)
c: Theo đề, ta có hệ phương triunfh:
\(\left\{{}\begin{matrix}x_1-x_2=6\\x_1+x_2=-3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x_1=3\\x_1+x_2=-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x_1=1,5\\x_2=-3-1,5=-4,5\end{matrix}\right.\)
\(x_1\cdot x_2=m\)
=>\(m=1,5\cdot\left(-4,5\right)=-6,75\left(nhận\right)\)
d: Theo Vi-et, ta có:
\(x_1+x_2=-3\)
=>\(x_2+5=-3\)
=>\(x_2=-8\)