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:
