Question
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