Question

Solve 3x2 + 4x = −5.

A) the quantity of negative 2 plus or minus i square root 11 all over 3
B) the quantity of negative 2 plus or minus 4i square root 3 all over 3
C) the quantity of negative 2 plus or minus 2 square root 11 all over 3
D) the quantity of negative 2 plus or minus 4i square root 3 all over 3

Answer 1

A) the quantity of negative 2 plus or minus i square root 11 all over 3

Explanation:

formula: x = [-b ±√(b²-4ac)]/2a

The given quadratic equation be,

3x² + 4x = -5

⇒ 3x² + 4x + 5 = 0

Solution:

a = 3, b = 4 and c = 5

x = [-b ±√(b²-4ac)]/2a

x= [-4 ±√(4²-4*3*5)]/2*3

x = [-4 ±√-44]/6

x = [-4 ±2i√11]/6

x = [-2 ±i√11]/3

Therefore the correct answer is option A) the quantity of negative 2 plus or minus i square root 11 all over 3

Answer 2

`x=(-2\pm √(11)i )/(3)`

Explanation:

The given equation is

`3x^2+4x=-5`

We rewrite in the general quadratic equation form to get,

`3x^2+4x+5=0`

By comparing to
`ax^2+bx+c=0`, we have

`a=3,b=4,c=5`

We can solve using the quadratic formula, which is given by

`x=(-b\pm √(b^2-4ac) )/(2a)`

We substitute the values to obtain;

`x=(-4\pm √(4^2-4(3)(5)) )/(2(3))`

`x=(-4\pm √(16-60) )/(6)`

`x=(-4\pm √(-44) )/(6)`

`x=(-4\pm 2√(11)i )/(6)`

`x=(-2\pm √(11)i )/(3)`

The correct answer is A.