If-a-R-and-the-equation-3-x-2-2-x-a-2-0-has-no-integral-solution-then-all-possible-value-of-a-lie-in-the-interval-a-1-0-U-0-1-b-1-2-c-2-1-d-2-U-2-

Question Number 57389 by rahul 19 last updated on 03/Apr/19

I f a ϵ R a n d t h e e q u a t i o n :

- 3 {x}^{2} + 2 {x} + a^{2} = 0 h a s n o i n t e g r a l

s o l u t i o n, t h e n a l l p o s s i b l e v a l u e o f a

l i e i n t h e i n t e r v a l :

(a) (- 1, 0) U (0, 1) (b) (1, 2)

(c) (- 2, - 1) (d) (- \infty, - 2) U (2, \infty)

Answered by einsteindrmaths@hotmail.fr last updated on 03/Apr/19

{x} \in [0.1 [s o i s t h e s a m e t o s a y - 3 y^{2} + 2 y + a^{2} = 0 h a s n o s o l u t i o n]

i n [0.1 [t h e s o l u t i o n o f - 3 y^{2} + 2 y + a^{2} = 0 a r e [- 2 + \sqrt{(4 + 12 a^{2})}] / - 6 a n d

[- 2 - \sqrt{(4 + 12 a^{2})}] / - 6 o n l y (2 + \sqrt{(4 + 12 a^{2}})) / 6 i s g r e a t e r t h a n] z e r

s o w e w a n t [2 + \sqrt{(4 + 12 a^{2})}] / 6 < 1 => \sqrt{(4 + 12 a^{2})} < 4 ===> 12 a^{2} < 12

Commented by rahul 19 last updated on 03/Apr/19

t h a n k s s i r!