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Let pa n dq be the roots of the equation...

Let pa n dq be the roots of the equation `x^2-2x+A=0` and let ra n ds be the roots of the equation `x^2-18 x+B=0`. If `p

Text Solution

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The correct Answer is:
`A = -3, B = 77`
Given, `p + q = 2, pq = A`
and it is given that p,q,r, s are in an AP.
Therefore, let `p = q -3d, q =a -d, r =a +d`
and `s = a + 3d`
Since, `p lt q lt r lt s`
We have, `d gt 0`
Now, `2 = p + q = a - 3d + a -d = 2a - 4d`
`rArr a - 2d = 1`....(i)
Again, `18 = r + s = a + d + a + 3d`
`18 = 2a + 4d`
`rArr 9 = a + 2d`...(iii)
On subtracting Eq. (i) from Eq. (ii), we get
`8 = 4d rArr d = 2`
On putting in Eq. (ii), we get `a = 5`
`:' p = q - 3d = 5 - 6 = -1`
`q = a -d = 5 - 2 = 3`
`r = a + d = 5 + 2 = 7`
and `s = a+ 3d = 5 + 6 = 11`
Therefore, `A = pq = -3 and B = rs = 77`
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