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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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      Log On


   

Question 15696: Please can you help with this question:
Given that, for all values of x: f%28x%29=3x%5E2%2B12x%2B5=p%28x%2Bq%29%5E2%2Br
Find the values of p,q and r
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Given that, for all values of x: f%28x%29=3x%5E2%2B12x%2B5=p%28x%2Bq%29%5E2%2Br
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.=f%28x%29=3x%5E2%2B12x%2B5=r.h.s.=p%28x%2Bq%29%5E2%2Br=px%5E2%2B2%2Ap%2Aq%2Ax%2Bp%2Aq%5E2%2Br
hence 3=p
12 = 2p*q or...... q=12/2*p = 12/2*3 = 12/6 =2
5= p%2Aq%5E2%2Br= 3*2^2+r=12+r...or.....r=5-12 = -7