Question

1. Solve.

x^2+9x+2=0

Enter your answers, as exact values, in the boxes.


2. What is the solution of the equation when solved over the complex numbers?

x^2+24=0

Answer 1

1. using the quadratic formula you get -9+/-sqrt(9^2-4*(1*2))/2*1

this simplies to x = -9 +/- sqrt(73)/2

x = -0.22799812 and -8.77200187

2. complex numbers have the letter i with them

using the quadratic formula

you get 0 +/- sqrt(0^2-4*(1*24))/2*1

x = -2i sqrt(6) and 2i sqrt(6)

Answer 2

Answer and explanation:

1) Solve :
`x^2+9x+2=0`

Applying quadratic formula,

`x=(-b\pm√(b^2-4ac))/(2a)`

Here, a=1 , b=9, c=2

`x=(-9\pm√(9^2-4(1)(2)))/(2(1))`

`x=(-9\pm√(81-8))/(2)`

`x=(-9\pm√(73))/(2)`

`x=(-9+√(73))/(2),(-9-√(73))/(2)`

`x=-0.227,-8.772`

2) Given :
`x^2+24=0`

To find : What is the solution of the equation when solved over the complex numbers?

Solution :

Quadratic equation,
`x^2+24=0`

Subtract 24 both side,

`x^2+24-24=-24`

`x^2=-24`

Taking root both side,

`x=√(-24)`

`x=\pm 2√(6)i`

The solution of the equation is
`x=2√(6)i,-2√(6)i`