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Question: If a&b are the roots of the equation, x<sup>2</sup> –2px + q = 0 and g and d be those of the equatio...

If a&b are the roots of the equation, x2 –2px + q = 0 and g and d be those of the equation, x2 –2rx + s = 0 and if

a, b, g, d be in A.P., then (s –q) is equal to-

A

p2 – r2

B

p2 –q2

C

q2 – p2

D

r2 –p2

Answer

r2 –p2

Explanation

Solution

a –3d a – d a + d a + 3d

a b g d

2a – 4d = 2p 2a + 4d = r

(a – 3d) (a – d) = q (a + d) (a + 3d) = s

a – 2d = p a + 2d = r

s – q = a2 + 4da + 3d2

– (a2 – 4ad + 3d2)

= +8 (ad)

= – (p2 – r2) = r2 – p2