Question

Show that the roots of the equation x^2 + 2 ( a + b ) x + 2 ( a^2 + b^2

) = 0

are unreal.​

Answer 1

Step-by-step explanation:

For unreal roots D<0

b

2

−4ac<0

B=2(a+b) C=2(a

2

+b

2

)

B

2

−4AC<0 A=1

4(a+b)

2

−4×1×2(a

2

+b

2

)

4a

2

+4b

2

+8ab−8a

2

−8b

2

8ab−4a

2

−4b

2

=−4(a−b)

2

<0

Hence roots are unreal.

Answer 2

Answer:-

Given:-

• The equation x² + 2 ( a + b ) x + 2 ( a² + b² ) = 0

To find:-

• The roots of the equation are unreal

Solution:-

Here,

For unreal roots D < 0

Use quadratic formula

b² - 4ac < 0

b = 2 ( a + b )

c = 2 ( a² + b² )

b² - 4ac < 0

⇒4 ( a + b )² - 4 × 1 × 2 ( a² + b² )

⇒4a² + 4b² + 8ab - 8a² - 8b²

⇒8ab - 4a² - 4b²

⇒ - 4 ( a - b )² < 0

Therefore, the roots are unreal