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


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