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If there are two values of a which makes...

If there are two values of a which makes determinant,
`Delta=|(1,-2,5),(2,a,-1),(0,4,2a)|=86` then the sum of these number is

A

`4`

B

`5`

C

`-4`

D

`9`

Text Solution

Verified by Experts

The correct Answer is:
C
We have
`Delta=|(1,-2,5),(2,a,-1),(0,4,2a)|=86`
`implies 1(2a^(2)+4)-2(-4a-20)+0=86` [expanding along first column]
`implies 2a^(2)+4+8a+40=86`
`implies 2a^(2)+8a+44-86=0`
`implies a^(2)+4a-21=0`
`implies a^(2)+7a-3a-21=0`
`= (a+7)(a-3)=0`
`a=-7` and `3`
`:.` Required sum `=-7+3=-4`
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