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A line through (2, 2) and the axes form a triangle of area A α units. Then, the intercepts on the axes made by the line are roots of the equation

(a) x2 - αx + α = 0

(b) x2 + αx + 2α = 0

(c)  x2 -αx + 2α = 0

(d)  x2 + αx - 2α = 0

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Best answer

Correct option (c),(d)

Explanation :

Let x/b + y/b = 1

be the equation of the line which forms a triangle with the coordinate axes of area α sq. unit. Since the line passes through (2, 2), we have

2/a + 2/b = 1 ...(1)

We have 1/2|ab| = α so that

ab = ±2α  ....(2)

now, from Eq.(2)

2a + 2b = ab = 2α

Therefore

a + b = α  ...(3)

Hence, from Eqs. (2) and (3), a and b are the roots of the equation  x2 - αx + 2α = 0. Therefore 

2a + 2b = -2α

a + b = -α

Hence a and b are roots of the equation

x2 + αx - 2α = 0

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