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

Step-by-step explanation:

The given equation is

We rewrite in the general quadratic equation form to get,

By comparing to , we have

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

We substitute the values to obtain;

The correct answer is A.

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

Step-by-step 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

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

answer: the answer is 110