Question

Nature of roots of the equation X2+2X+4=0 is

Answer 1

Answer:

the root of eqn is unreal

Answer 2

hi mate,

X^2+2X+4=0

Solving x^2+2x+4 = 0

by the Quadratic Formula .

- B ± √ B^2-4AC

x = ————————

2A

In our case, A = 1

B = 2

C = 4

Accordingly, B^2 - 4AC =

4 - 16 =

-12

Applying the quadratic formula :

-2 ± √ -12

x = ——————

2

Both i and -i are the square roots of minus 1

Accordingly,√ -12 =

√ 12 • (-1) =

√ 12 • √ -1 =

± √ 12 • i√ 12 = √ 2•2•3 =

± 2 • √ 3

√ 3 , rounded to 4 decimal digits, is 1.7321

So now we are looking at:

x = ( -2 ± 2 • 1.732 i ) / 2

Two imaginary solutions :

x =(-2+√-12)/2=-1+i√ 3 = -1.0000+1.7321i

or:

x =(-2-√-12)/2=-1-i√ 3 = -1.0000-1.7321i

Two solutions were found :

x =(-2-√-12)/2=-1-i√ 3 = -1.0000-1.7321i

x =(-2+√-12)/2=-1+i√ 3 = -1.0000+1.7321i

i hope it helps you.