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) {3 x}^{2} - 19 x - 6 ⩽ 0

(ii) {2 x}^{2} - 5 x - 3 ⩾ 0

Commented by sandy_suhendra last updated on 25/Feb/17

is that true for (i) {3 x}^{2} - 19 x - 6 ⩽ 0

not {3 x}^{2} - 19 x + 6 ?

Answered by sandy_suhendra last updated on 25/Feb/17

(ii) {2 x}^{2} - 5 x - 3 = 0

(2 x + 1) (x - 3) = 0

2 x + 1 = 0 or x - 3 = 0

x = - \frac{1}{2} x = 3

+ + + + - - - - + + + +

______∙______∙______

- \frac{1}{2} 3

x ⩽ - \frac{1}{2} or x ⩾ 3