Question

find roots of QE x²+4x+5=0​

Answer 1

$\huge\underline\red{Answer:-}$

x = - 5 and 1.

Step By Step Explanation:-

→ x² + 4x - 5 = 0

→ x² + 4x = 5

→ x² + 2(4/2)x = 5

→ x² + 2(2)x + 2² = 5 + 2²

→ (x + 2)² = 9

→ x + 2 = ±3

Case 1:

If 3 is positive,

→ x = 3 - 2 = 1

Case 2:

If 3 is negative,

→ x = - 3 - 2 = - 5

Hence, x = - 5 and 1.

______________________

Answer 2

Solution:-

=> x² + 4x + 5 = 0

we solve it by complete square method.

=> x² + 4x = - 5

Add both side 4

=> x² + 4x + 4 = - 5 + 4

=> x² + 4x + 4 = - 1

=> x² + 2x + 2x + 4 = - 1

=> x( x + 2 ) + 2( x + 2 ) = - 1

=> ( x + 2 ) ( x + 2 ) = - 1

=> ( x + 2 )² = - 1

=> x + 2 = √- 1

( in Math, i is called the imaginary

unit. It satisfies i² = -1. Both i and

-i are the square roots of -1 .

since a square root has two values, one positive and the other negative).

=> x = √1 - 2

so now

=> x = - 2 + √1 • i

=> x = - 2 - √1 • i

Note :- ( i used because of imaginary number. )

i hope it helps you.