Let p and q be the 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. The value of (A+B) equals

Q. Let p and q be the 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, B respectively equal to:

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Let p and q be the roots of the equation x2−2x+A=0 and let r and s be the roots of the equation x2−18x+B=0. If p < q < r < s are in A.P. then A + B =

The correct option is A 74p + q = 2, pq = A, R + s = 18, rs = B. If d is the common difference of the A.P q = p + d, r = p + 2 d, s = p + 3d, p + q = 2 ⇒ 2p + d = 2 r + s = 18 ⇒ 2p + 5d = 18. Solving d = 4, p = - 1, q = 3, r = 7, s = 11 A + B = pw + rs = - 3 + 77 = 74

Let p and q be the 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 A.P. then A + B =

The correct option is A 74
p + q = 2, pq = A, R + s = 18, rs = B. If d is the common difference of the A.P
q = p + d, r = p + 2 d, s = p + 3d, p + q = 2 $\Rightarrow$ 2p + d = 2
r + s = 18 $\Rightarrow$ 2p + 5d = 18. Solving d = 4, p = - 1, q = 3, r = 7, s = 11
A + B = pw + rs = - 3 + 77 = 74