For-two-real-and-distinct-solutions-to-y-3-y-ax-2-b-As-can-be-seen-from-graph-in-comment-below-if-a-gt-0-b-lt-3-while-if-a-lt-0-b-gt-3-

Question Number 13359 by ajfour last updated on 19/May/17

F o r t w o r e a l a n d d i s t i n c t

s o l u t i o n s t o :

y = 3

y = {a x}^{2} + b

A s c a n b e s e e n f r o m g r a p h i n

c o m m e n t b e l o w,

i f a > 0, b < 3

w h i l e i f a < 0, b > 3 .

Commented by ajfour last updated on 19/May/17

Commented by ajfour last updated on 19/May/17

Commented by mrW1 last updated on 19/May/17

3 = {a x}^{2} + b

x^{2} = \frac{3 - b}{a} > 0

\Rightarrow a > 0 a n d b < 3

o r

\Rightarrow a < 0 a n d b > 3

Commented by ajfour last updated on 19/May/17

v e r y s t r a i g h t, t h a n k s .

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