What-is-the-value-of-a-and-b-when-3x-4-6x-3-ax-2-bx-12-is-completely-divisible-by-x-2-3-

Question Number 115117 by bobhans last updated on 23/Sep/20

W h a t i s t h e v a l u e o f a a n d b w h e n

3 x^{4} + 6 x^{3} - {a x}^{2} - b x - 12 i s c o m p l e t e l y

d i v i s i b l e b y x^{2} - 3 ?

Answered by john santu last updated on 23/Sep/20

W r i t e y o u r p o l y n o m i a l a s

p (x) = x^{2} (3 x^{2} + 6 x - a) - b x - 12

n o w c o m p u t i n g t h e r e m a i n d e r o f

t h e d i v i s i o n i s e a s y . S u b s t i t u t i n g

3 f o r x^{2} \Rightarrow 3 (3.3 + 6 x - a) - b x - 12 = 0

\Rightarrow 3 (6 x + 9 - a) - b x - 12 = 0 x + 0

{\begin{cases} 18 - b = 0 \to b = 18 \\ 27 - 3 a - 12 = 0 \to a = 5 \end{cases}