Question

verify that 3 -1 -1/3 are the zeroes of the cubic polynomial p(x)=3x^3-5x^2-11x-3 and then verify the relationship between the zeroes and the coefficients.​

Answer 1

Answer:

first put x=3

3(3)³-5(3)²-11(3)-3

then -1

and -1/3

in all cases resultant value=0

sum of zeros=-b/a

3+(-1)+(-1/3)=-(-5)/3

2-1/3=5/3

5/3=5/3

sum of product of zeros=c/a

3(-1)+(-1)(-1/3)+(-1/3)(3)=-11/3

-3+1/3-1=-11/3

-4+1/3=-11/3

-11/3=-11/3

product of zeros=-d/a

3(-1)(-1/3)=-(-3)/3

-3× -1/3=1

-1×-1=1

1=1

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