If α, β are the roots of the equation 2x2

If α, β are the roots of the equation 2x² - 3x + 1 = 0, form an
equation whose roots are α and β
β α

As we know that ,
∴ α, β are the roots of the equation 2x² - 3x + 1 = 0

∴ α + β =	3	........... ( 1 )
	2

and αβ =	1	........... ( 2 )
	2

We are to form a quadratic equation whose roots are

α	and	β
β	and	α

S = sum of the roots =	α	+	β	=	α² + β²	=	( α + β )² - 2αβ
	β		α		αβ		αβ

∴ Using ( 1 ) and ( 2 ) , we get

S =	5	x	2	=	5
	4		1		2

P = Product of the roots =	α	×	β	= 1
	β		α

Hence the required quadratic equation is x² − (sum of the roots)x + (Product of the roots) = 0

⇒ x² -	5	x + 1 = 0
	2

⇒ 2x² - 5x + 2 = 0.