If `a,b,c,d gt 0` , `x in R` and `(a^(2)+b^(2)+c^(2))x^(2)-2(ab+bc+cd)x+b^(2)+c^(2)+d^(2) le 0`, then `|{:(33,14,loga),(65,27,logb),(97,40,logc):}|=`

Options

A. `1`
B. `-1`
C. `0`
D. none of these

Answer

C

Explanation

`(c )` We have
`(a^(2)+b^(2)+c^(2))x^(2)-2(ab+bc+cd)x+b^(2)+c^(2)+d^(2) le 0`
`implies(ax-b)^(2)+(bx-c)^(2)+(cx-d)^(2) le 0`
`implies(ax-b)^(2)+(bx-c)^(2)+(cx-d)^(2) = 0`
`implies(b)/(a)=(c )/(b)=(d)/(c )=x`
`impliesb^(2)=ac` or `2logb=loga+logc`,
Now, `|{:(33,14,loga),(65,27,logb),(97,40,logc):}|` [Apply `R_(1)toR_(1)+R_(3)-2R_(2)`]
`=|{:(0,0,0),(65,27,logb),(97,40,logc):}|`