The identity 4(z + 7)(2z – 1) = Az² + Bz + C holds for all real values of z. Find the value of A² – B – C.

40

4(z + 7)(2z – 1) = Az² + Bz + C 

According to the question,

4(z + 7)(2z – 1)  = 8z² + 52z - 28

On comparing this expression with Az² + Bz + C , 

A = 8, B = 52 and C = -28

The value of A² – B – C = (8)² - 52 - (-28) = 64 - 52 + 28 = 40