Find the missing term. The roots of x2 − ( ____) + 34 are 5 ± 3i.

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 
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, 
x² + (-m)x + 34 
x² − mx + 34 ← Now, substitute 10 for m 
x² − 10x + 34 ← ANSWER