(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


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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
	$(1) x^2 −x−4050=0→ { (p),(q) :} ⇔p^2 = p+4050 then p^2 +q = p+4050+q = p+q +4050 = 1+4050 = 4051 ;(by Vieta′s rule )★$
	$(1) x^{2} - x - 4050 = 0 \to {\begin{cases} p \\ q \end{cases}$ $\Leftrightarrow p^{2} = p + 4050$ $t h e n p^{2} + q = p + 4050 + q$ $= p + q + 4050$ $= 1 + 4050 = 4051; (b y {V i e t a}^{'} s$ $r u l e) ★$
	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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