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Let a and b the roots of the equation x 2 – 10cx – 11d = 0 and those of x 2 - 10 ax – 11b = are c, d then the value of a + b + c + d, when a ≠ b ≠ c ≠ d, is.

Let a and b the roots of the equation x2 – 10cx – 11d = 0 and those of x2  - 10 ax – 11b = are c, d then the value of a + b + c + d, when a ≠ b ≠ c ≠ d, is.

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
9 years ago
Sol. Roots of x2 – 10cx – 11d = 0 are a and b
⇒ a + b = 10c and ab = -11d
Similarly c and d are the roots of x2 – 10ax – 11b = 0
⇒ c + d = 10a and cd = -11b
⇒ a + b + c + d = 10( a + c) and abcd = 121 bd
⇒ b + d = 9(a + c) and ac = 121
Also we have a2 – 10 ac – 11d = 0 and c2 – 10ac – 11b = 0
⇒ a2 + c2 – 20ac – 11(b + d) = 0
⇒ (a + c)2 – 22 x 121 – 99 (a + c) = 0
⇒ a + c = 121 or – 22
For a + c = -22, we get a = c
∴ rejecting this value we have a + c = 121
∴ a + b + c + d = 10 (a + c)

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