How do you find the number of possible positive real zeros and negative zeros then determine the rational zeros given #f(x)=x^3-7x-6#?

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Answer 1 · 2017-10-23T12:23:48

Rational zeros of #f(x)# are #x=-1 , x=-2 and x=3#

#f(x)=x^3-7x-6# . Here constant number is #-6# and leading

Coefficient is #1# . Factors of #6# are #1,2,3,6,# and factors of #1#

Are # 1 :. # Possible rational zeros are # +-(1,2,3,6)/( 1 ) :. #

Possible rational zeros are #+-(1,2,3,6)# On checking,

#f (1)= -12 , f(-1) =0 , f(2) = -12, f(-2)=0 , f(3)=0 :.

Zeros are #x=-1 , x=-2 and x=3# hence

#(x+1),(x+2) and (x-3)# are factors.

#:.f(x)=x^3-7x-6 =(x+1)(x+2)(x-3) #

Rational zeros of #f(x)# are #x=-1 , x=-2 and x=3# [Ans]