Question

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

Answer 1

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=(-b\pm√(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=(-16\pm√(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