Question

Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Als
verify the relationship between the zeroes and coefficients in each case :
(I)2x3 + x2 - 6x + 2; 2, 1, - 2,
1, -2, (ii)x3 – 4x² + 5x – 2; 2, 1, 1.​

Answer 1

(i)2x3 + x2 - 6x + 2

2,1,-2 are not the zeroes of the cubic polynomial

Relationship between zeroes and coefficients

Sum of zeroes=-(coefficient of x^2)/coefficient of x^3=-1/2

Product of zeroes=constant term/coefficient of x^3=2/2=1

Sum and product of zeroes taken at the time

=Coefficient of x/coefficient of x^3=-6/2=-3

(ii)x3 – 4x² + 5x – 2

2,1 are the zeroes of the cubic polynomial x3 – 4x² + 5x – 2

Relationship between zeroes and coefficients

Sum of zeroes=-(coefficient of x^2)/coefficient of x^3=-(-4)/1=4

Product of zeroes=-(constant term)/coefficient of x^3=-(-2)/1=2

Sum and product of zeroes taken at the time

=Coefficient of x/coefficient of x^3=5/1=5

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