Đáp án + Giải thích các bước giải:
`a)` `3x^2+x-2=0`
`<=>3x^2+3x-2x-2=0`
`<=>3x(x+1)-2(x+1)=0`
`<=>(x+1)(3x-2)=0`
`<=>`\(\left[ \begin{array}{l}x+1=0\\3x-2=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=-1\\x=\dfrac{2}{3}\end{array} \right.\)
Vậy `S={-1;2/3}`
`b)` `4x^2+5x-6=0`
`<=>4x^2+8x-3x-6=0`
`<=>4x(x+2)-3(x+2)=0`
`<=>(x+2)(4x-3)=0`
`<=>`\(\left[ \begin{array}{l}x+2=0\\4x-3=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=-2\\x=\dfrac{3}{4}\end{array} \right.\)
Vậy `S={-2;3/4}`
`c)` `6x^2+20x+6=0`
`<=>2(3x^2+10x+3)=0`
`<=>3x^2+10x+3=0`
`<=>3x^2+9x+x+3=0`
`<=>3x(x+3)+(x+3)=0`
`<=>(x+3)(3x+1)=0`
`<=>`\(\left[ \begin{array}{l}x+3=0\\3x+1=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=-3\\x=-\dfrac{1}{3}\end{array} \right.\)
Vậy `S={-3;-1/3}`
`d)` `8x^2+2x-3=0`
`<=>8x^2-4x+6x-3=0`
`<=>4x(2x-1)+3(2x-1)=0`
`<=>(2x-1)(4x+3)=0`
`<=>`\(\left[ \begin{array}{l}2x-1=0\\4x+3=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=\dfrac{1}{2}\\x=-\dfrac{3}{4}\end{array} \right.\)
Vậy `S={1/2;-3/4}`
`e)` `10x^2-11x-6=0`
`<=>10x^2-15x+4x-6=0`
`<=>5x(2x-3)+2(2x-3)=0`
`<=>(2x-3)(5x+2)=0`
`<=>`\(\left[ \begin{array}{l}2x-3=0\\5x+2=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=\dfrac{3}{2}\\x=-\dfrac{2}{5}\end{array} \right.\)
Vậy `S={3/2;-2/5}`
`f)` `10x^2+17x-6=0`
`<=>10x^2+20x-3x-6=0`
`<=>10x(x+2)-3(x+2)=0`
`<=>(x+2)(10x-3)=0`
`<=>`\(\left[ \begin{array}{l}x+2=0\\10x-3=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=-2\\x=\dfrac{3}{10}\end{array} \right.\)
Vậy `S={-2;3/10}`.
