find values a , b , c such that: −1≤ ax^2 +bx +c ≤ 1 and ((6b^( 2) + 8 a^( 2) )/3) is Max...


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Question Number 146062 by mnjuly1970 last updated on 10/Jul/21

$f i n d v a l u e s a, b, c s u c h t h a t :$ $- 1 ⩽ a x^{2} + b x + c ⩽ 1$ $a n d \frac{6 b^{2} + 8 a^{2}}{3} i s M a x . . .$
Commented by mr W last updated on 10/Jul/21

${i t}^{'} s n o t p o s s i b l e w i t h a \neq 0 a n d b \neq 0$ $t h a t - 1 ⩽ a x^{2} + b x + c ⩽ 1 .$ $t h a t m e a n s, s u c h t h a t$ $- 1 ⩽ a x^{2} + b x + c ⩽ 1$ $w e m u s t h a v e a = b = 0 .$ $- 1 ⩽ c ⩽ 1 .$ $s i n c e m a x = \frac{6 b^{2} + 8 a^{2}}{3} = 0 \Rightarrow c = 0$
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