The identity 4(z + 7)(2z – 1) = Az2 + Bz + C holds for all real values of z. Find the value of A2 – B – C .
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 40
Given:
4(z + 7)(2z – 1) = Az2 + Bz + C ...(i)
Explanation:
Taking LHS of equation (i), 4(z + 7)(2z – 1)
⇒ 4(2z2 - z + 14z - 7)
⇒ 8z2 + 52z - 28 ....(ii)
Comparing equation (ii) with RHS of equation (i),
⇒ 8z2 + 52z - 28 = Az2 + Bz + C
So, A = 8, B = 52 and C= -28
Now, A2 – B – C = (8)2 - 52 - (-28)
⇒ 64 - 52 + 28
⇒ 92 - 52 = 40
Hence the required value is 40.