Question

Verify 3, -1,-1/3 are zeroes of 3x^3-5x^2-11x-3 and verify the relation between zeroes and coefficients.

Answer 1

put 3, -1, -1/3 in the given polynomial in place of x and try to find the answer 0 ..if answer comes out to be 0 then they the zeros of the polynomials otherwise not ...!!.....and for relationship ...use the given relationship that are given in the ncert for cubic polynomial

Answer 2

we can get that equation
 f(x) =3x^3-5x^2-11x-3
x = 3 as 
f(3) =3(3)^3 - 5(3)^2 -11(3) -3
        = 81 - 45 - 36
        =0
thereby x-3  is factor of f(x)//
 x= -1,
f(-1) =3(-1)^3 - 5(-1)^2 -11(-1) -3
        = -3 -5 + 11 -3
        =0//
thereby x+1  is factor of f(x)//
 x= -1/3,
f(-1/3) =3(-1/3)^3 - 5(-1/3)^2 -11(-1/3) -3
        = -1/9 -5/9  + 11/3 -3
        =-6/9 +(11 -9)/3
        =  (-6 +6)/9
        =0//
thereby x+1/3  is factor of f(x)//

(x+1/3)(x-3)(x +1)
[x^2 - 3x +1/3x -1](x+1)
[x^2 - 8/3x - 1](x +1)
x^3  + x^2[-8/3 + 1]  -x[1 +8/3]  -1
x^3 - x^2*5/3 - 11/3x  -1
3x^3 - 5x^2 -11x -1//