If P(x) is a polynomial such thatP(x)+P(2x)=5×2−18 then limx→3 P(x)x−3 is

# If $P\left(x\right)$ is a polynomial such that$P\left(x\right)+P\left(2x\right)=5{x}^{2}-18$ then $\underset{x\to 3}{lim} \frac{P\left(x\right)}{x-3}$ is

1. A
2. B
3. C
4. D

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)

### Solution:

Clearly, $P\left(x\right)$ is a quadratic polynomial. So, let

$P\left(x\right)=a{x}^{2}+bx+c$ Then

and , Hence $\underset{x\to 3}{lim} \frac{P\left(x\right)}{x-3}=\underset{x\to 3}{lim} \frac{{x}^{2}-9}{x-3}=\underset{x\to 3}{lim} \left(x+3\right)=6$

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)