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

If α, β are the roots of the quadratic equation x² - 8x + k = 0, find the value of k such the α² + β² = 40

According to question ,
∵ α, β are the roots of the equation x² - 8x + 1 = 0

∴ α + β =	- b	=	- ( - 8 )	= 8
	a		1

and αβ =	c	=	k	= k
	a		1

Now, α² + β² = ( α + β )² - 2αβ
⇒ 40 = (8)² -2k ⇒ 2k= 24 ⇒ k = 12.
Thus , the value of k is 12 .