dashiexp57 dashiexp57
  • 18-03-2022
  • Mathematics
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f(x) = (2x − 3)(x + 6)(5x + 6) has zeros at x = -6, x = -6/5 and x =3/2.
What is the sign of f on the interval - 6

fx 2x 3x 65x 6 has zeros at x 6 x 65 and x 32 What is the sign of f on the interval 6 class=

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xenia168
xenia168 xenia168
  • 18-03-2022

Answer:

Step-by-step explanation:

f ( - 7 ) = [ 2 ( - 7 ) - 3]( - 7 + 6 )[ 5 ( - 7 ) + 6 ] = ( - 17 )( - 1 )( - 29 ) < 0 , Negative

f ( - 5 ) = [ 2 ( - 5 ) - 3]( - 5 + 6 )[ 5 ( - 5 ) + 6 ] = ( - 13 )( + 1 )( - 19 ) > 0 , Positive

f ( - 1 ) = [ 2 ( - 1 ) - 3]( - 1 + 6 )[ 5 ( - 1 ) + 6 ] = ( - 5 )( + 5 )( + 1 ) < 0 , Negative

The answer is (A) " f " is always POSITIVE

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