MATH SOLVE

4 months ago

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

Accepted Solution

A:

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

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