Question

If `b^(2) -ac lt 0 and a gt 0` then the value of the determinant is
A. positive
B. negative
C. zero
D. `b^(2)+ae`

Answer 1

Correct Answer - 2
We have `|{:(a,b,ax+by),(b,c,bx+cy),(ax+by,bx+cy,0):}|`
`|{:(" "a," "b," "0),(" "b," "c," "0),(ax+by,bx+cy,-(ax^(2)+2bxy+cy^(2))):}|`
[Applying `C_(3)toC_(3)-xC_(1)-yC_(2)`]
`=-(ax^(2)+2bx+cy^(2))(ac-b^(2))`
`(1)/(a)(b^(2)-ac)[(ax+by)^(2)+Y^(2)(ac-b^(2))]lt0`
`[therefore b^(2)-aclt 0 and agt 0]`