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

Step-by-step 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

Answer:

The roots are

$x = - 2 + \frac{3}{2} \: i \: \: \: \: or \: \: \: \: x = - 2 - \frac{3}{2} \: i$

Step-by-step 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

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

Separate the real and imaginary parts

That's

$x = \frac{ - 16}{8} \pm \frac{12}{8} \: i \\ x = - 2\pm \frac{3}{2} i$

We have the final answer as

$x = - 2 + \frac{3}{2} \: i \: \: \: \: or \: \: \: \: x = - 2 - \frac{3}{2} \: i$

Hope this helps you