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Its too simple. In order to get check whether it is zero or not just substitute the zeros of polynoomial values in the equation 4x^3-5x^2-23x+6=0 x=(-2) 4(-2)^3-5(-2)^2-23(-2)+6=0 =4(-8)-5(4)+46+6 =-32-20+52 =-52+52=0 === -2 is zero of the polynomial ==== 4x^3-5x^2-23x+6=0 x=1/4 4(1/4)^3-5(1/4)^2-23(1/4)+6=0 4(1/64)-5(1/16)-23/4+6 1/16-5/16-23/4+6 LCM is 16 1-5-92+96/16 -97+97/16 0/16==0 1/4 is the zero of polynomial Last thing to be answered that is 3 root for the equation for this we need to divided any of the root we got with polynomial given. x=-2 can be written as (x+2) on dividing 4x^3-5x^2-23x+6 with x+2 the quotient is 4x^2-13x+3 on finding roots for it we get x=1/4 and x=3 therefore the three roots are 1/4,-2 and 3