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-

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