Question

X2 + 10x + 89 = 0
what are the roots of the equation in the simplest a+bi form?

Answer 1

The answer is

`x = - 5 + 8 \: i \: \: \: \: or \: \: \: \: x = - 5 - 8 \: i \\`

Explanation:

x² + 10x + 89 = 0

Using the quadratic formula

`x = \frac{ - b\pm \sqrt{ {b}^(2) - 4ac} }{2a}`

From the question

a = 1 , b = 10 , c = 89

Substitute the values into the above formula and solve

We have

`x = \frac{ - 10\pm \sqrt{ {10}^(2) - 4(1)(89)} }{2(1)} \\ = ( - 10\pm √(100 - 356) )/(2) \\ = ( - 10\pm √( - 256) )/(2) \\ = (10\pm 16 \: i)/(2)`

Separate the real and imaginary part

That's

`x = - (10)/(2) \pm (16)/(2) \: i \\ x = - 5\pm8 \: i`

We have the final answer as

`x = - 5 + 8 \: i \: \: \: \: or \: \: \: \: x = - 5 - 8 \: i \\`

Hope this helps you