If f(x)= x^2 +ax+b. if f(1)= 3 and and one of the roots of the eqiation f(x)= 0 doubles the other, find the positive values of a and b.


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Question Number 210013 by otchereabdullai@gmail.com last updated on 28/Jul/24

$I f f (x) = x^{2} + a x + b . i f f (1) = 3 a n d$ $a n d o n e o f t h e r o o t s o f t h e e q i a t i o n$ $f (x) = 0 d o u b l e s t h e o t h e r, f i n d t h e$ $p o s i t i v e v a l u e s o f a a n d b .$
	Answered by mr W last updated on 28/Jul/24

	$s a y t h e o n e r o o t i s p, t h e n t h e o t h e r$ $r o o t i s 2 p .$ $p + 2 p = - a \Rightarrow p = - \frac{a}{3}$ $p \times 2 p = b \Rightarrow 2 a^{2} = 9 b$ $f (1) = 1^{2} + a + b = 3 \Rightarrow a + b = 2$ $2 a^{2} = 9 (2 - a)$ $\Rightarrow 2 a^{2} + 9 a - 18 = 0$ $\Rightarrow a = \frac{3}{2}, - 6 (r e j e c t e d)$ $\Rightarrow b = \frac{1}{2}$
	Commented by otchereabdullai@gmail.com last updated on 28/Jul/24

	$t h a n k s s o o m u c h P r o f W$
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