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Let alpha,beta be the roots of x^2-x+p=0...

Let `alpha,beta` be the roots of `x^2-x+p=0a n dgamma,delta` are roots of `x^2-4x+q=0.` If `alpha,beta,gamma,delta` are in G.P., then the integral value of `pa n dq` , respectively, are `-2,-32` b. `-2,3` c. `-6,3` d. `-6,-32`

A

`-2, -32`

B

`-2, 3`

C

`-6, 3`

D

`-6, -32`

Text Solution

Verified by Experts

The correct Answer is:
A
`{:(alpha + beta = 1),(alpha beta = p):}}` and `{:(lamda + delta = 4),(lamda delta = q):}}`
Let r be the common ratio.
Since, `alpha, beta, gamma and delta` are in GP.
Therefore, `beta = ar, gamma = ar^(2)`
and `delta = ar^(3)`
Then, `alpha + ar = 1 rArr alpha (1 + r) = 1`...(i)
and `ar^(2) + ar^(3) = 4 rArr ar^(2) (1 +r) = 4`...(ii)
From Eqs. (i) and (ii), `r^(2) = 4 rArr r = +-2`
Now, `alpha.ar = p and ar^(2) .ar^(3) = q`
On putting `r = -2`, we get
`alpha = -1, p = -2 and q = -32`
Again putting `r = 2`, we get `alpha = 1//3 and p = -(2)/(9)`
since, q and p are integers
Therefore, we take `p = -2 and q = -32`
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