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Question Number 10795 by j.masanja06@gmail.com last updated on 25/Feb/17

$$\mathrm{by}\mathrm{use}\mathrm{sketching}\mathrm{determine}\mathrm{the}\mathrm{range}$$$$\mathrm{or}\left(\mathrm{ranges}\right)\mathrm{of}\mathrm{the}\mathrm{value}\mathrm{x}\mathrm{can}\mathrm{take}\mathrm{for}$$$$\mathrm{each}\mathrm{of}\mathrm{the}\mathrm{following}\mathrm{inqualities}$$$$\left(\mathrm{i}\right){3\mathrm{x}}^2-19\mathrm{x}-6⩽0$$$$\left(\mathrm{ii}\right){2\mathrm{x}}^2-5\mathrm{x}-3⩾0$$

Commented by sandy_suhendra last updated on 25/Feb/17

$$\mathrm{is}\mathrm{that}\mathrm{true}\mathrm{for}\left(\mathrm{i}\right){3\mathrm{x}}^2-19\mathrm{x}-6⩽0$$$$\mathrm{not}{3\mathrm{x}}^2-19\mathrm{x}+6?$$

Answered by sandy_suhendra last updated on 25/Feb/17

$$\left(\mathrm{ii}\right){2\mathrm{x}}^2-5\mathrm{x}-3=0$$$$(2\mathrm{x}+1)(\mathrm{x}-3)=0$$$$2\mathrm{x}+1=0\mathrm{or}\mathrm{x}-3=0$$$$\mathrm{x}=-\frac{1}{2}\mathrm{x}=3$$$$++++----++++$$$$\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\bullet \mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\bullet \mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}$$$$-\frac{1}{2}3$$$$\mathrm{x}⩽-\frac{1}{2}\mathrm{or}\mathrm{x}⩾3$$

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