SOLUTION: Q- For what value of p and q, the expession, {{{ x^4-14x^3+71x^2+px+q }}} is a perfect square?? please help me in this problem in detail. I have problem in these type of proble

Algebra ->  Square-cubic-other-roots -> SOLUTION: Q- For what value of p and q, the expession, {{{ x^4-14x^3+71x^2+px+q }}} is a perfect square?? please help me in this problem in detail. I have problem in these type of proble      Log On


   

Question 726937: Q- For what value of p and q, the expession, +x%5E4-14x%5E3%2B71x%5E2%2Bpx%2Bq+ is a perfect square??
please help me in this problem in detail. I have problem in these type of problems.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x%5E4-14x%5E3%2B71x%5E2%2Bpx%2Bq+ = %28x%5E2%2Bax%2Bb%29%5E2

Multiply the right side out and you have the identity:

+x%5E4-14x%5E3%2B71x%5E2%2Bpx%2Bq+ = +x%5E4%2B2ax%5E3%2B%28a%5E2%2B2b%29x%5E2%2B2abx%2Bb%5E2+

The x4's terms cancel.

Equating terms in x³:

2a = -14
 a = -7

Equating terms in x²:

a²+2b = 71

Substituting a = -7

(-7)²+2b = 71
   49+2b = 71
      2b = 22
       b = 11

Equating terms in x:

2ab = p

Substituting a = -7 and  b = 11

2(-7)(11) = p
     -154 = p 

Equating constant terms:

b² = q
11² = q
121 = q

Answer: p = -154, q = 121

Edwin