1)
f(x)=3x²-7x+2
[tex]3x^2-7x+2\\\\\Delta=25\rightarrow \sqrt{\Delta}=5\\\\x_1=\frac{7-5}{6}\ \vee \ x_2=\frac{7+5}{6}\\\\x_1=\frac{1}{3}\ \vee \ x_2=2\\\\f(x)=3(x-\frac{1}{3})(x-2)\\[/tex]
2)
f(x)=x²+3x-28
[tex]x^2+3x-28\\\\\Delta=121\rightarrow \sqrt{\Delta}=11\\\\x_1=\frac{-3-11}{2}\ \vee \ x_2=\frac{-3+11}{2}\\\\x_1=-7\ \vee \ x_2=4\\\\f(x)=(x+7)(x-4)\\[/tex]
3)
f(x)=2x^2-1
[tex]2x^2-1\\\\\Delta=8\rightarrow \sqrt{\Delta}=2\sqrt{2}\\\\x_1=\frac{-2\sqrt{2}}{4}\ \vee \ x_2=\frac{2\sqrt{2}}{4}\\\\x_1=-\frac{\sqrt{2}}{2}\ \vee \ x_2=\frac{\sqrt{2}}{2}\\\\f(x)=2(x+\frac{\sqrt{2}}{2})(x-\frac{\sqrt{2}}{2})\\[/tex]
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1)
f(x)=3x²-7x+2
[tex]3x^2-7x+2\\\\\Delta=25\rightarrow \sqrt{\Delta}=5\\\\x_1=\frac{7-5}{6}\ \vee \ x_2=\frac{7+5}{6}\\\\x_1=\frac{1}{3}\ \vee \ x_2=2\\\\f(x)=3(x-\frac{1}{3})(x-2)\\[/tex]
2)
f(x)=x²+3x-28
[tex]x^2+3x-28\\\\\Delta=121\rightarrow \sqrt{\Delta}=11\\\\x_1=\frac{-3-11}{2}\ \vee \ x_2=\frac{-3+11}{2}\\\\x_1=-7\ \vee \ x_2=4\\\\f(x)=(x+7)(x-4)\\[/tex]
3)
f(x)=2x^2-1
[tex]2x^2-1\\\\\Delta=8\rightarrow \sqrt{\Delta}=2\sqrt{2}\\\\x_1=\frac{-2\sqrt{2}}{4}\ \vee \ x_2=\frac{2\sqrt{2}}{4}\\\\x_1=-\frac{\sqrt{2}}{2}\ \vee \ x_2=\frac{\sqrt{2}}{2}\\\\f(x)=2(x+\frac{\sqrt{2}}{2})(x-\frac{\sqrt{2}}{2})\\[/tex]