If the equations x2 + 2x - 3 = 0 and x2 + 3x

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If the equations x² + 2x - 3 = 0 and x² + 3x - k = 0 have a common root, then the non - zero value of k is :

1. 1
2. 2
3. 3
4. 4

Correct Option: D

As per the given above question , we can say that
Let, α be a common root of the given equations.
Putting the value of x = α , α² + 2α - 3 = 0 and α² + 3α - k = 0
By cross - product method , we get

∴	α²	=	α	=	1
	-2k + 9		-3 + k		3 -2

So, α² =	9 - 2k	and α =	k - 3
	1		1

So, ( 9 - 2k ) = ( k - 3 )² ⇒ k² - 4k = 0
⇒ k( k - 4 ) = 0, so k = 4.
Hence , the non-zero value of k is 4 .