SOLUTION: Please can you help with this question: Given that, for all values of x: {{{f(x)=3x^2+12x+5=p(x+q)^2+r}}} Find the values of p,q and r

Question 15696: Please can you help with this question:
Given that, for all values of x:
Find the values of p,q and r
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Given that, for all values of x:
Find the values of p,q and r
the given equation is a second degree polynomial in x and should have 2 roots or it should be satisfied by 2 values of x . but it is given that it is true for all values of x . so it is an identity . so coefficients of corresponding terms on either side of the identity shall be equal
l.h.s.==r.h.s.==
hence 3=p
12 = 2p*q or...... q=12/2*p = 12/2*3 = 12/6 =2
5= = 3*2^2+r=12+r...or.....r=5-12 = -7

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