Question

Solve -x2 - 3x = 4 over the set of complex numbers

Answer 1

`\bold{x=(-3\pm i√(7))/(2)}`

Explanation:

Given quadratic equation is:

`-x^2 - 3x = 4`

Rewriting the given equation:

`-x^2 - 3x - 4 = 0`

OR

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

Solution of a quadratic equation represented as
`ax^2+bx+c=0` is given as:

`x=(-b\pm√(b^2-4ac))/(2a)`

Comparing the given equation with standard equation:

a = 1

b = 3

c = 4

So, the roots are:

`x=(-3\pm√(3^2-4* 1 * 4))/(2* 1)\\\Rightarrow x=(-3\pm√(9-16))/(2)\\\Rightarrow x=(-3\pm√(-7))/(2)`

`√(-7 )` can be written as
`7√(-1)`

and
`√(-1) = i`

So,
`√(-7) = i\sqrt7`

The numbers containing
`i` in them, are called as complex numbers.

Therefore, the roots of the equation can be written as:

`\Rightarrow \bold{x=(-3\pm i√(7))/(2)}`