Question 726937
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Let {{{ x^4-14x^3+71x^2+px+q }}} = {{{(x^2+ax+b)^2}}}

Multiply the right side out and you have the identity:

{{{ x^4-14x^3+71x^2+px+q }}} = {{{ x^4+2ax^3+(a^2+2b)x^2+2abx+b^2 }}}

The x<sup>4</sup>'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</pre>