Given-that-f-x-x-3-x-2-ax-b-and-g-x-2x-3-9x-2-3ax-b-have-a-common-factor-x-1-where-a-and-b-are-constands-Find-the-values-of-a-and-b-hence-find-other-factors-of-f-x-

Question Number 35419 by Rio Mike last updated on 18/May/18

G i v e n t h a t

f (x) = x^{3} - x^{2} + a x + b a n d

g (x) = 2 x^{3} - 9 x^{2} - 3 a x + b h a v e a

c o m m o n f a c t o r (x - 1) w h e r e a a n d

b a r e c o n s t a n d s . F i n d t h e v a l u e s

o f a a n d b h e n c e f i n d o t h e r f a c t o r s

o f f (x)

Answered by ajfour last updated on 18/May/18

a + b = 0

b - 3 a = 7

\Rightarrow a = \frac{- 7}{4}, b = \frac{7}{4}

f (x) = x^{2} (x - 1) - \frac{7}{4} (x - 1)

f (x) = (x + \frac{\sqrt{7}}{2}) (x - 1) (x - \frac{\sqrt{7}}{2})

Facebook Tweet Pin