Question

Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.

Answer 1

Answer:

Option B.

{–9 + i√225 / 24, –9 – i√225 / 24}

Step-by-step explanation:

12a² + 9a + 7 = 0

Using formula method, the solutions to the equation can be obtained as follow:

Coefficient of a² (a) = 12

Coefficient of a (b) = 9

Constant (c) = 7

a = –b ±√(b² – 4ac) / 2a

a = –9 ±√(9² – 4 × 12 × 7) / 2 × 12

a = –9 ±√(81 – 336) / 24

a = –9 ±√(– 225) / 24

Recall

–225 = –1 × 225

Thus,

–9 ±√(– 225) / 24 = –9 ±√(–1 × 225)/24

Recall

√(–1 × 225) = √–1 × √225 = i√225

Thus,

–9 ±√(–1 × 225)/24 = –9 ± i√225/24

Therefore,

a = –9 ± i√225/24

a = –9 + i√225 / 24 or –9 – i√225 / 24

Therefore, the solutions to the equation are:

{–9 + i√225 / 24, –9 – i√225 / 24}