Question

giúp mik từ bài 9 -> 15 vs ạ

Answer 1

Bài 11:

Bài 9:

Bài 12:

Đặt \(f\left(x\right)=3x^2-2\left(m+1\right)x-2m^2+3m-2\)

\(\Delta=\left[-2\cdot\left(m+1\right)\right]^2-4\cdot3\cdot\left(-2m^2+3m-2\right)\)

\(=4m^2+8m+4-12\left(-2m^2+3m-2\right)\)

\(=4m^2+8m+4+24m^2-36m+24\)

\(=28m^2-28m+28=28\left(m^2-m+1\right)\)

\(=28\left(m^2-m+\dfrac{1}{4}+\dfrac{3}{4}\right)\)

\(=28\left(m-\dfrac{1}{2}\right)^2+21>=21>0\forall m\)

Để f(x)>=0 với mọi x thì \(\left\{{}\begin{matrix}\Delta< =0\\a>0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}28\left(m-\dfrac{1}{2}\right)^2+21< =0\left(vôlý\right)\\3>0\end{matrix}\right.\)

=>\(m\in\varnothing\)