4p2 + 7 = 12p

(viii) 4p² + 7 = 12p

Sol. 4p² + 7 = 12p

∴  4p² – 12p = –7

Dividing both the sides by 4 we get,

p² – 3p = ^-7/₄       .....(i)

Third term = ( ½ ×  coefficient of p)²

= ( ½ × - 3)²

= (^-3/₂)²

= ⁹/₄

Adding 9/4 to both sides of (i) we get,

p² – 3p  + ⁹/₄ = ^-7/₄   + ⁹/₄

∴ (p – ³/₂)² =     ²/₄

∴ p - ³/₂ = ±√(²/₄)  

∴ p - ³/₂ = ±√²/₂

∴ p = ³/₂   ±  √²/₂

∴ p = ^(3±√2) /₂

∴ p = ^(3+√2) /₂  OR  ^{(3 - √2)} /₂