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

(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

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 )★

Answered by bemath last updated on 15/Jul/20

(2)(fog)(4)= f(g(4))  ⇒g(4)= 7.4 + 8 = 36   ⇒f(36) = 24 →((7.36+q)/2) = 24  q = 48−252 = −204 ★