Question

What are the solutions of 3x2 + 15 = –6x?

A) –1 ± i
B) –1 ± 2i
C) –2 ± i
D) –2 ± 2i

Answer 1

Choice B is the answer.

Explanation:

We have given a quadratic equation.

3x² + 15 = –6x

3x²+6x+15 = 0

We have to find the solution of above equation.

Taking 3 common from above expression, we have

3(x²+2x+5) = 0

x²+2x+5 = 0

From above equation, a = 1,b = 2 and c = 5

x = (-b±√b²-4ac ) / 2a is quadratic formula to solve equations.

Putting values in above formula ,we have

x = (-2±√(2)²-4(1)(5) ) / 2(1)

x = (-2±√4-20 ) / 2

x = (-2±√-16) / 2

x = (-2±√-1√16) / 2 ∵ i = √-1

x = (-2±4i) / 2

x = 2(-1±2i) / 2

x = -1±2i

Hence, the solution of given equation is -1±2i.

Answer 2

B) –1 ± 2i

Explanation:

The equation; 3x² + 15 = –6x

Could be written as

3x²-6x + 15 = 0

Using the quadratic formula to solve for x

x = (-6 ± √(6²-4×3×15))/(2×3)

= (-6 ± √(36 - 180))/6

= (-6 ± √(-144))/6

but √-1 = i

Therefore;

= (-6 ± √(144)i)/6

= (-6 ± 12i)/6

= -1 ± 2i