If the equation 2x2 – 7x + 12 = 0 has two roots α

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If the equation 2x² – 7x + 12 = 0 has two roots α and β, then the value of α + β is :
β α

2x² – 7x + 12 = 0

∴ α + β =	7
	2

αβ =	12	= 6
	2

[In equation ax² + bx + c = 0 ]

∴ α + β =	-b	and	αβ =	c
	a			a

∴	α	+	β	=	α² + β²
	β		α		αβ

⇒	α	+	β	=	( α + β )² - 2αβ
	β		α		αβ

⇒	α	+	β	=	( 7 / 2)² - 2 × 6
	β		α		6

⇒	α	+	β	=	( 49 / 4) - 12
	β		α		6

⇒	α	+	β	=	49 - 48	=	1
	β		α		24		24

If the equation 2x² – 7x + 12 = 0 has two roots α and β, then the value of	α	+	β	is :
	β		α