JEE Advanced Mathematics question

Mathematics Quadratic Equations and Inequalities JEE Advanced

Let P, A, B, C be four collinear points in order, the distances of A, B, C from P being respectively. If the equation has one root double the other then

(A)B divides AC in the ratio internallyCorrect
(B)C divides AB in the ratio externally
(C)B divides AC in the ratio internallyCorrect
(D)none of these

Answer: (A),(C)

Solution

Since the points are in order, . The coefficients add to , so is a root. The product of the roots gives the other root:

x = .

"One root double the other" means the other root is or .

- gives . Then $AB = b - a =

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Question ID VK-110122