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Determinants

Question
CBSEENMA12034460
Wired Faculty App

If x = – 9 is a root of
open vertical bar table row straight x cell space space 3 end cell cell space space 7 end cell row 2 cell space space straight x end cell cell space space 2 end cell row 7 cell space 6 end cell cell space straight x end cell end table close vertical bar space equals 0 comma
find the other roots.

Solution
The given equation is
open vertical bar table row straight x cell space 3 end cell cell space 7 end cell row 2 cell space straight x end cell cell space 2 end cell row 7 cell space 6 end cell cell space straight x end cell end table close vertical bar space equals space 0
or          open vertical bar table row cell straight x plus 9 end cell cell straight x plus 9 end cell cell straight x plus 9 end cell row 2 straight x 2 row 7 6 straight x end table close vertical bar space equals 0 comma space space by space space space straight R subscript 1 plus straight R subscript 2 plus straight R subscript 3
or space left parenthesis straight x plus 9 right parenthesis space open vertical bar table row 1 cell space 1 end cell cell space 1 end cell row 2 cell space straight x end cell cell space 2 end cell row 7 cell space 6 end cell cell space straight x end cell end table close vertical bar space equals space 0 or space left parenthesis straight x plus 9 right parenthesis thin space open vertical bar table row 1 0 cell space space space 0 end cell row cell 2 space end cell cell space space space straight x minus 2 end cell cell space space space 0 end cell row 7 cell negative 1 end cell cell straight x minus 7 end cell end table close vertical bar space equals 0 comma space by space straight C subscript 2 minus straight C subscript 1 comma space space straight C subscript 3 minus straight C subscript 1 space or space left parenthesis straight x plus 9 right parenthesis space open square brackets left parenthesis 1 right parenthesis thin space left parenthesis straight x minus 2 right parenthesis thin space left parenthesis straight x minus 7 right parenthesis close square brackets space equals space 0 space space space space space space space space space space space space space space space left square bracket Product space of space diagonal space elements right square bracket or space space left parenthesis straight x minus 2 right parenthesis thin space left parenthesis straight x minus 7 right parenthesis thin space left parenthesis straight x plus 9 right parenthesis space equals space 0 therefore space space space space straight x space equals space 2 comma space space 7 comma space space minus 9 because space space space straight x space equals space minus 9 space is space given space root therefore space space other space roots space are space 2 comma space 7.

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