# Show that -2 and 1/4 are zeroes of the polynomial 4x*-5x*-23x+6 also find the third zero of the polynomial

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by agnayaprem

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by agnayaprem

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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