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2x^(2) + 3x - alpha - 0 " has roots "-2 ...

`2x^(2) + 3x - alpha - 0 " has roots "-2 and beta " while the equation "x^(2) - 3mx + 2m^(2) = 0 " has both roots positive, where " alpha gt 0 and beta gt 0.`
If `beta,2,2m `are in GP, then what is the value of `beta sqrt(m)` ?

A

1

B

2

C

4

D

6

Text Solution

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The correct Answer is:
A
` beta= 1/2`
` beta, 2, 2"m are in GP".`
` rArr 2/beta = (2m)/2`
` rArr m= 2/beta = 2 xx 2/1`
` rArr m = 4`
` rArr betasqrtm = 1/2 xx sqrt(4) = 1`
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