Question

Solve 14x2 + 42x + 70 = 0.

A) 1 plus or minus i square root 11
B) the quantity of negative 3 plus or minus i square root 29 all over 2
C) the quantity of negative 3 plus or minus 2i square root 29 all over 2
D) the quantity of negative 3 plus or minus i square root 11 all over 2

Answer 1

d

Explanation:

Answer 2

`x = -(3)/(2) + (√(11))/(2)i` or
`x = -(3)/(2) - (√(11))/(2)i`

Explanation:

`14x^2 + 42x + 70 = 0`

First, divide both sides by 14.

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

There are no two real numbers whose product is 5 and whose sum is 3, so this polynomial is not factorable. We use the quadratic formula.

`x = (-b \pm √(b^2 - 4ac))/(2a)`

We have a = 1; b = 3; c = 5.

`x = (-3 \pm √((-3)^2 - 4(1)(5)))/(2(1))`

`x = (-3 \pm √(9 - 20))/(2)`

`x = (-3 \pm √(-11))/(2)`

`x = (-3 \pm i√(11))/(2)`

`x = -(3)/(2) + (√(11))/(2)i` or
`x = -(3)/(2) - (√(11))/(2)i`