Let p and q be roots of the equation x 2 - 2 x + A = 0 and let r and s be the roots of the equation x 2 - 18 x + B = 0 . If p q r s are in arithmetic progression, then A and B are

Question

Let p and q be roots of the equation x 2 - 2 x + A = 0 and let r and s be the roots of the equation x 2 - 18 x + B = 0 . If p q r s are in arithmetic progression, then A and B are, - 3 , - 77, 3 , - 77, - 3 , 77, 3 , 77

MARKS App · Accepted Answer

x 2 - 2 x + A = 0 ⇒ x = 1 ± 1 - A ∴ p = 1 - 1 - A , q = 1 + 1 - A Similarly, r = 9 - 81 - B , s = 9 + 81 - B p , q , r , s are in AP . ∵ q - p = s - r ⇒ 2 1 - A = 2 81 - B ⇒ B = 80 + A and q - p = r - q ⇒ 3 1 - A = 8 - 81 - B ⇒ A = - 3 , B = 77

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