Question

What are the roots of the equation 9x^2 + 54x +82 = 0 in simplest a + bi form?​

Answer 1

The roots are

`x = - 3 + (1)/(3) i \: \: \: or \: \: \: x = - 3 - (1)/(3) i \\`

Explanation:

9x² + 54x + 82 = 0

Using the quadratic formula

That's

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

From the question

a = 9 , b = 54 , c = 82

Substitute the values into the above formula and solve

That's

`x = \frac{ - 54\pm \sqrt{ {54}^(2) - 4(9)(82)} }{2(9)} \\ x = ( - 54\pm √(2916 - 2952) )/(18) \\ x = ( - 54\pm √( - 36) )/(18) \\ x = ( - 54\pm 6i)/(18)`

Separate the real and imaginary parts

That's

`x = - (54)/(18) \pm (6)/(18) \: i \\ x = - 3\pm (1)/(3) i`

We have the final answer as

`x = - 3 + (1)/(3) i \: \: \: or \: \: \: x = - 3 - (1)/(3) i \\`

Hope this helps you