If one root of the quadratic equation 2x2 + Px + 4 = 0

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If one root of the quadratic equation 2x² + Px + 4 = 0 is 2, find the second root and value of P.

1. 1, - 6
2. 1, 6
3. −1, 6
4. −1, −6

Correct Option: A

Here ,The given equation is 2x² + Px + 4 = 0 .......( ⅰ )
⇒ P(x) = 0 , where P(x) = 2² + Px + 4 = 0
If 2 is a root of P(x) = 0, then P(2) = 0
Putting x = 2 in equation ( ⅰ ) , we get
⇒ 2(2)² + P(2) + 4 = 0
⇒ 8 + 2P + 4 = 0
⇒ 2P = - 12

⇒	P =	-12	= - 6
		2

Hence the given equation is
2x² - 6x + 4 = 0 { ∴ Putting the value of P in eq. ( ⅰ ) }
⇒ 2x² - 2x - 4x + 4 = 0
⇒ 2x ( x - 1 ) - 4( x - 1 ) = 0
⇒ 2( x - 2 ) ( x - 1 ) = 0
⇒ x = 1 or x = 2
Hence second root is 1.