If P(x) is a polynomial such thatP(x)+P(2x)=5x2−18 then limx→3 P(x)x−3 is

Solution:

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

$P (x) = a x^{2} + b x + c$ Then

$\begin{array}{l} P (x) + P (2 x) = 5 x^{2} - 18 \\ \Rightarrow a x^{2} + b x + c + 4 a x^{2} + 2 b x + c = 5 x^{2} - 18 \\ \Rightarrow 5 a x^{2} + 3 b x + 2 c = 5 x^{2} - 18 \\ \Rightarrow 5 a = 5, 3 b = 0 and 2 c = - 18 \\ \Rightarrow a = 1, b = 0 and c = - 9 \\ ∴ P (x) = x^{2} - 9 \end{array}$

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

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

Solution:

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