Question

What are the roots of the equation 4x^2 + 16x + 25 = 0 in simplest a + bi form?​

Answer 1

Answer:-2 + 3i/2, and -2-3i/2

Explanation:

Apply the quadratic formula.

We have (-16 +-sqrt(16^2-4*4*25))/8.

Simplifying, we have (-16+-12i)/8.

Thus, the roots are -2 + 3i/2, and -2-3i/2

Answer 2

The roots are

`x = - 2 + (3)/(2) \: i \: \: \: \: or \: \: \: \: x = - 2 - (3)/(2) \: i \\`

Explanation:

4x² + 16x + 25 = 0

Using the quadratic formula

That's

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

From the question

a = 4 , b = 16 , c = 25

Substitute the values into the above formula and solve

We have

`x = \frac{ - 16\pm \sqrt{ {16}^(2) - 4(4)(25)} }{2(4)} \\ x = ( - 16\pm √(256 - 400) )/(8) \\ x = ( - 16\pm √( - 144) )/(8) \\ x = ( - 16\pm12 \: i)/(8) \\`

Separate the real and imaginary parts

That's

`x = ( - 16)/(8) \pm (12)/(8) \: i \\ x = - 2\pm (3)/(2) i`

We have the final answer as

`x = - 2 + (3)/(2) \: i \: \: \: \: or \: \: \: \: x = - 2 - (3)/(2) \: i \\`

Hope this helps you