If α, β are the roots of the equation x2

If α, β are the roots of the equation x² - 5x + 6 = 0, construct a quadratic equation whose roots are
1 , 1 .
α β

As per the given above question , we can say that
Comparing x² - 5x + 6 = 0 with ax² - bx + c = 0 , we get
a = 1, b = - 5, c = 6

∴ α + β =	- b	=	5	= 5
	a		1

αβ =	c	= 6
	a

Now, we are to form an equation whose roots are

1	,	1	.
α		β

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

x²

x +

= 0

x² -		α + β		x +		1		= 0
		αβ				αβ

x² -	5	x +	1	= 0
	6		6

6x² - 5x + 1 = 0
Thus , required equation is 6x² - 5x + 1 = 0 .