Let $P(x)$ be a quadratic polynomial such that

$\left|\begin{array}{ll} P(0) & P(1) \\ P(0) & P(2) \end{array}\right|=0$

Let $P(0)=2$ and $P(1)+P(2)+P(3)=14$ . Then $P(4)$ equals

Question

Let $P(x)$ be a quadratic polynomial such that $\left|\begin{array}{ll} P(0) & P(1) \ P(0) & P(2) \end{array}\right|=0$ Let $P(0)=2$ and $P(1)+P(2)+P(3)=14$. Then $P(4)$ equals

Accepted Answer

C - -6. The determinant P(0)(P(2)-P(1)) = 0 with P(0) = 2 gives P(1) = P(2). With P = ax^2+bx+2 this means b = -3a. The sum condition 14a+6b+6 = 14 gives a = -2, b = 6, so P(4) = -32+24+2 = -6.

Answer

A - -14

Answer

B - 30

Answer

D - 16

Let \(P(x)\) be a quadratic polynomial such that \(\left|\begin{array}{ll} P(0) & P(1) \\ P(0) & P(2) \end{array}\right|=0\) Let \(P(0)=2\) and \(P(1)+P(2)+P(3)=14\). Then \(P(4)\) equals

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