If x⁴ + 2x³ + ax² + bx + 9 is a perfect square where a and b are positive real numbers, then the value of a and b is?

A. a = 5, b = 6

B. a = 6, b = 7

C. a = 7, b = 7

D. a = 7, b = 8

Answer: Option B

Solution(By Examveda Team)

$$\eqalign{ & {x^4} + 2{x^3} + a{x^2} + bx + 9 \cr & {\text{Put }}x = 1 \cr & = 1 + 2 \times 1 + a + b + 9 \cr & = 1 + 2 + a + b + 9 \cr & = 13 + a + b \cr} $$
To make a perfect square numbers value of a + b must be either 3 or 13
Now, option (B) a = 6, b = 7
$$\eqalign{ & \therefore a + b = 13 \cr & {\text{make perfect square}} \cr & \left( {25 = {5^2}} \right) \cr} $$