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)


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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

	$a + b = 0$ $b - 3 a = 7$ $\Rightarrow a = \frac{- 7}{4}, b = \frac{7}{4}$ $f (x) = x^{2} (x - 1) - \frac{7}{4} (x - 1)$ $f (x) = (x + \frac{\sqrt{7}}{2}) (x - 1) (x - \frac{\sqrt{7}}{2})$
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