Question

Verify that 2, 1, 1 are zeroes of polynomial x' - 4x? + 5x 2. Also verify the relationship between the zeroes and the coefficients.

Answer 1

P(x)=x^3-4x^2+5x-2

2,1,1 are the zeroes of the cubic polynomial P(x)=x^3-4x^2+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 a time

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

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