$$a+b=3$$ $$ab=2\times 1=2$$

$$a=1$$ $$b=2$$

$$\left(2x^{2}+x\right)+\left(2x+1\right)$$

$$x\left(2x+1\right)+2x+1$$

$$\left(2x+1\right)\left(x+1\right)$$

$$x=-\frac{1}{2}$$ $$x=-1$$

$$2x^{2}+3x+1=0$$

$$x=\frac{-3±\sqrt{3^{2}-4\times 2}}{2\times 2}$$

$$x=\frac{-3±\sqrt{9-4\times 2}}{2\times 2}$$

$$x=\frac{-3±\sqrt{9-8}}{2\times 2}$$

$$x=\frac{-3±\sqrt{1}}{2\times 2}$$

$$x=\frac{-3±1}{2\times 2}$$

$$x=\frac{-3±1}{4}$$

$$x=-\frac{2}{4}$$

$$x=-\frac{1}{2}$$

$$x=-\frac{4}{4}$$

$$x=-1$$

$$x=-\frac{1}{2}$$ $$x=-1$$

$$2x^{2}+3x+1=0$$

$$2x^{2}+3x+1-1=-1$$

$$2x^{2}+3x=-1$$

$$\frac{2x^{2}+3x}{2}=-\frac{1}{2}$$

$$x^{2}+\frac{3}{2}x=-\frac{1}{2}$$

$$x^{2}+\frac{3}{2}x+\left(\frac{3}{4}\right)^{2}=-\frac{1}{2}+\left(\frac{3}{4}\right)^{2}$$

$$x^{2}+\frac{3}{2}x+\frac{9}{16}=-\frac{1}{2}+\frac{9}{16}$$

$$x^{2}+\frac{3}{2}x+\frac{9}{16}=\frac{1}{16}$$

$$\left(x+\frac{3}{4}\right)^{2}=\frac{1}{16}$$

$$\sqrt{\left(x+\frac{3}{4}\right)^{2}}=\sqrt{\frac{1}{16}}$$

$$x+\frac{3}{4}=\frac{1}{4}$$ $$x+\frac{3}{4}=-\frac{1}{4}$$

$$x=-\frac{1}{2}$$ $$x=-1$$

$$x ^ 2 +\frac{3}{2}x +\frac{1}{2} = 0$$

$$r + s = -\frac{3}{2} $$ $$ rs = \frac{1}{2}$$

$$r = -\frac{3}{4} - u$$ $$s = -\frac{3}{4} + u$$

$$(-\frac{3}{4} - u) (-\frac{3}{4} + u) = \frac{1}{2}$$

$$\frac{9}{16} - u^2 = \frac{1}{2}$$

$$-u^2 = \frac{1}{2}-\frac{9}{16} = -\frac{1}{16}$$

$$u^2 = \frac{1}{16}$$ $$u = \pm\sqrt{\frac{1}{16}} = \pm \frac{1}{4} $$

$$r =-\frac{3}{4} - \frac{1}{4} = -1$$ $$s = -\frac{3}{4} + \frac{1}{4} = -0.500$$