The roots of x^2-()+34 are
5+3i

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:

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step-by-step explanation:

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