Question

The quadratic equation whose roots are the a and b intercepts of the line passing through (1, 1) and making a triangle of area A with the coordinate axes, is

• A. x² + Ax +2A = 0
• B. x² – 2Ax + 2A = 0
• C. x² – Ax + 2A = 0
• D. None of these

Answer 1

Answer: (B)

x² – 2Ax + 2A = 0

Answer 2

Equatio n of the line, having intercepts a and b on the x and the y axes respectively, is

x/a + y/b = 1. . . . . . (1)

It passes through (1, 1) ⇒ 1/a + 1/b = 1.

Since the area of the triangle formed by the lines and the axes is A,

ab = 2A. . . . . .(2)

From (1) & (2) we get a + b = 2A.

Here a, b are the roots of x² – (a+b)x + ab = 0 or x² – 2Ax + 2A = 0