Here ,The given equation is 2x² + Px + 4 = 0 .......( ⅰ )
⇒ P(x) = 0 , where P(x) = 2 ² + 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

Correct Option: A

Here ,The given equation is 2x² + Px + 4 = 0 .......( ⅰ )
⇒ P(x) = 0 , where P(x) = 2 ² + 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

From the given equations , we know that
Ⅰ. x² - 1 = 0
⇒ x² = 1

Ⅱ. y² + 4y + 3 = 0
⇒ y² + y + 3y + 3 = 0
⇒ y( y + 1) + 3( y + 1) = 0

Correct Option: B

From the given equations , we know that
Ⅰ. x² - 1 = 0
⇒ x² = 1
⇒ x = ± √1 = ± 1
Ⅱ. y² + 4y + 3 = 0
⇒ y² + y + 3y + 3 = 0
⇒ y( y + 1) + 3( y + 1) = 0
⇒ ( y + 1) ( y + 3)
⇒ y = -3 or -1
From above equations it is clear that x ≥ y is correct answer .

According to given question , we have
Ⅰ. x³ - 371 = 629
⇒ x = √1000 = 10
Ⅱ. y³ - 543 = 788
⇒ y = √1331 = 11

Correct Option: C

According to given question , we have
Ⅰ. x³ - 371 = 629
⇒ x = √1000 = 10
Ⅱ. y³ - 543 = 788
⇒ y = √1331 = 11
From above both equations it is clear that x < y is correct answer .

According to question ,we can say that
From equation Ⅰ. 2x² + 11x + 12 = 0
⇒ 2x² + 8x + 3x + 12 = 0
⇒ 2x( x + 4) + 3( x + 4) = 0

From equation Ⅱ. 5y² + 27y + 10 = 0
⇒ 5y² + 25y + 2y + 10 = 0
⇒ 5y( y + 5 ) + 2( y + 5 ) = 0

Correct Option: E

According to question ,we can say that
From equation Ⅰ. 2x² + 11x + 12 = 0
⇒ 2x² + 8x + 3x + 12 = 0
⇒ 2x( x + 4) + 3( x + 4) = 0
⇒ ( 2x + 3) ( x + 4) = 0

According to question ,we can say that
From equation Ⅰ. x⁴ = 398 + 227 = 625

From equation Ⅱ. y² = 346 - 321 = 25

Correct Option: E

According to question ,we can say that
From equation Ⅰ. x⁴ = 398 + 227 = 625
⇒ x⁴ = 5⁴

From equation Ⅱ. y² = 346 - 321 = 25
⇒ y² = 5²