Answer:
We're given the roots of a quadratic function.
And, we are looking for the middle term.
Since the Quadratic Formula is used to determine the roots of a quadratic function, we can use the Quadratic Formula to get the value of the coefficient of the middle term.
       ax² + bx + c             ← Standard form ... Notice that there are two plus signs
        x² − (__) + 34            ← This is what we're given
         x² − mx + 34            ← This is what we know ... Now, put this in standard form
   ➊  x² + (-m)x + 34           ← a = 1, b = -m, c = 34
        -b ± √(b²-4ac)
x = ———————            ← Rewrite this as two fractions to fit the form of 5±3i
                2a
        -b        √(b²-4ac)
x = —— ± —————            ← Compare this to  5 ± 3i
         2a              2a
So,
         -b        -(-m)
      ——– = ——–– = 5  ⇒  m = 10a  ⇒  m = 10
          2a           2a
Therefore,
   ➊  x² + (-m)x + 34
        x² −   mx + 34           ← Now, substitute  10 for  m
        x² − 10x + 34           ← ANSWER
Step-by-step explanation: