If α and β are the roots of the equation x2

If α and β are the roots of the equation x² - 3λx + λ² = 0,
find λ if α² + β² = 7
4

Given that :- α, β are the roots of the equation x² - 3λx + λ² = 0
α + β = 3λ ....................( 1 )
and αβ = λ² ...................( 2 )

Now, α² + β² =	7	( given )
	4

⇒ ( α + β )² - 2αβ =	7
	4

⇒ ( 3λ)² - 2λ² =	7
	4

⇒ 7λ² =	7
	4

⇒ λ² =	1
	4

⇒ λ = ±	1	.
	2

Hence , required answer will be option A .

find λ if α² + β² =	7
	4

±	√7
	2

±	√3
	2