a)
[tex]W(x)=3ax^3-(2a-1)x+4\\\\W(2)=0\\\\3a*2^3-(2a-1)*2+4=0\\\\3a*8-2(2a-1)+4=0\\\\24a-4a+2+4=0\\\\20a+6=0\\\\20a=-6\ |:20\\\\a=-\frac{6}{20}\\\\a=-\frac{3}{10}[/tex]
b)
[tex]W(x)=(x-a)(2a-3x)\\\\W(-1)=0\\\\(-1-a)(2a-3*(-1))=0\\\\(-1-a)(2a+3)=0\\\\-1-a=0\quad\vee\quad2a+3=0\\\\-a=1\ |:(-1)\quad\vee\quad2a=-3\ |:2\\\\a=-1\quad\vee\quada=-\frac{3}{2}\\\\a\in\left\{-\frac{3}{2},-1\right\}[/tex]
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a)
[tex]W(x)=3ax^3-(2a-1)x+4\\\\W(2)=0\\\\3a*2^3-(2a-1)*2+4=0\\\\3a*8-2(2a-1)+4=0\\\\24a-4a+2+4=0\\\\20a+6=0\\\\20a=-6\ |:20\\\\a=-\frac{6}{20}\\\\a=-\frac{3}{10}[/tex]
b)
[tex]W(x)=(x-a)(2a-3x)\\\\W(-1)=0\\\\(-1-a)(2a-3*(-1))=0\\\\(-1-a)(2a+3)=0\\\\-1-a=0\quad\vee\quad2a+3=0\\\\-a=1\ |:(-1)\quad\vee\quad2a=-3\ |:2\\\\a=-1\quad\vee\quada=-\frac{3}{2}\\\\a\in\left\{-\frac{3}{2},-1\right\}[/tex]