1-If-p-and-q-are-the-roots-quadratic-equation-x-2-x-4050-0-find-the-value-of-p-2-q-2-if-f-x-7x-q-2-and-g-x-7x-8-fog-4-24-find-the-value-of-q-

Question Number 103458 by bobhans last updated on 15/Jul/20

(1) I f p a n d q a r e t h e r o o t s q u a d r a t i c

e q u a t i o n x^{2} - x - 4050 = 0, f i n d t h e v a l u e

o f p^{2} + q ?

(2) i f f (x) = \frac{7 x + q}{2} a n d g (x) = 7 x + 8;

(f o g) (4) = 24 . f i n d t h e v a l u e o f q

Answered by bemath last updated on 15/Jul/20

(1) x^{2} - x - 4050 = 0 \to {\begin{cases} p \\ q \end{cases}

\Leftrightarrow p^{2} = p + 4050

t h e n p^{2} + q = p + 4050 + q

= p + q + 4050

= 1 + 4050 = 4051; (b y {V i e t a}^{'} s

r u l e) ★

Answered by bemath last updated on 15/Jul/20

(2) (f o g) (4) = f (g (4))

\Rightarrow g (4) = 7.4 + 8 = 36

\Rightarrow f (36) = 24 \to \frac{7.36 + q}{2} = 24

q = 48 - 252 = - 204 ★

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