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by-use-sketching-determine-the-range-or-ranges-of-the-value-x-can-take-for-each-of-the-following-inqualities-i-3x-2-19x-6-0-ii-2x-2-5x-3-0-




Question Number 10795 by j.masanja06@gmail.com last updated on 25/Feb/17
by use sketching determine the range  or(ranges) of the value x can take for  each of the following inqualities  (i) 3x^2 −19x−6≤0  (ii)2x^2 −5x−3≥0
$$\mathrm{by}\:\mathrm{use}\:\mathrm{sketching}\:\mathrm{determine}\:\mathrm{the}\:\mathrm{range} \\ $$$$\mathrm{or}\left(\mathrm{ranges}\right)\:\mathrm{of}\:\mathrm{the}\:\mathrm{value}\:\mathrm{x}\:\mathrm{can}\:\mathrm{take}\:\mathrm{for} \\ $$$$\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{inqualities} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{3x}^{\mathrm{2}} −\mathrm{19x}−\mathrm{6}\leqslant\mathrm{0} \\ $$$$\left(\mathrm{ii}\right)\mathrm{2x}^{\mathrm{2}} −\mathrm{5x}−\mathrm{3}\geqslant\mathrm{0} \\ $$
Commented by sandy_suhendra last updated on 25/Feb/17
is that true for (i) 3x^2 −19x−6≤0   not 3x^2 −19x+6 ?
$$\mathrm{is}\:\mathrm{that}\:\mathrm{true}\:\mathrm{for}\:\left(\mathrm{i}\right)\:\mathrm{3x}^{\mathrm{2}} −\mathrm{19x}−\mathrm{6}\leqslant\mathrm{0}\: \\ $$$$\mathrm{not}\:\mathrm{3x}^{\mathrm{2}} −\mathrm{19x}+\mathrm{6}\:? \\ $$
Answered by sandy_suhendra last updated on 25/Feb/17
(ii) 2x^2 −5x−3=0         (2x+1)(x−3)=0           2x+1=0  or  x−3=0             x=−(1/2)           x=3  ++++    −−−−     ++++  ______•______•______               −(1/2)               3  x≤−(1/2)   or   x≥3
$$\left(\mathrm{ii}\right)\:\mathrm{2x}^{\mathrm{2}} −\mathrm{5x}−\mathrm{3}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\left(\mathrm{2x}+\mathrm{1}\right)\left(\mathrm{x}−\mathrm{3}\right)=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{2x}+\mathrm{1}=\mathrm{0}\:\:\mathrm{or}\:\:\mathrm{x}−\mathrm{3}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}=−\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}=\mathrm{3} \\ $$$$++++\:\:\:\:−−−−\:\:\:\:\:++++ \\ $$$$\_\_\_\_\_\_\bullet\_\_\_\_\_\_\bullet\_\_\_\_\_\_ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:−\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3} \\ $$$$\mathrm{x}\leqslant−\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\mathrm{or}\:\:\:\mathrm{x}\geqslant\mathrm{3} \\ $$

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