g(x)= 6x^2 − 5ax + b^2 given that g(x) has only two roots and are (x−1) and (x−2) find the value of a and b.Using (x−1) as a root detemine the extend to which (x−2) is a root (occurance as a root).


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Question Number 35513 by Rio Mike last updated on 19/May/18

$g (x) = 6 x^{2} - 5 a x + b^{2}$ $g i v e n t h a t g (x) h a s o n l y t w o r o o t s$ $a n d a r e (x - 1) a n d (x - 2)$ $f i n d t h e v a l u e o f a a n d b . U s i n g$ $(x - 1) a s a r o o t d e t e m i n e t h e$ $e x t e n d t o w h i c h (x - 2) i s a r o o t$ $(o c c u r a n c e a s a r o o t) .$
	Answered by Rasheed.Sindhi last updated on 19/May/18

	$g (x) = 6 x^{2} - 5 a x + b^{2}$ $∵ x - 1 is factor$ $g (1) = 6 {(1)}^{2} - 5 a (1) + b^{2} = 0$ $b^{2} - 5 a = - 6 . . . . . . . . . . A$ $∵ x - 2 is factor$ $g (2) = 6 {(2)}^{2} - 5 a (2) + b^{2} = 0$ $b^{2} - 10 a = 24 . . . . . . . . . . B$ $A - B : 5 a = - 30 \Rightarrow a = - 6$ $A \Rightarrow b^{2} - 5 (- 6) = - 6$ $b^{2} = - 6 - 30 = - 36$ $b = \pm 6 i$
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