Question

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

Answer 1

Answer:

The roots are

$x = - 3 + \frac{1}{3} i \: \: \: or \: \: \: x = - 3 - \frac{1}{3} i$

Step-by-step 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

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

Separate the real and imaginary parts

That's

$x = - \frac{54}{18} \pm \frac{6}{18} \: i \\ x = - 3\pm \frac{1}{3} i$

We have the final answer as

$x = - 3 + \frac{1}{3} i \: \: \: or \: \: \: x = - 3 - \frac{1}{3} i$

Hope this helps you