Question

verify that 1, - 1, - 3 are zeros of cubic polynomial x cube + 3 x square minus x minus 3 and check the relationship between zeros and the coefficients​

Answer 1

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

P(1)=(1)^3+3(1)^2-(1)-3

P(1)=1+3-1-3

P(1)=0

P(-1)=(-1)^3+3(-1)^2-(-1)-3

P(-1)=-1+3+1-3

P(-1)=0

P(-3)=(-3)^3+3(-3)^2-(-3)-3

P(-3)=-27+27+3-3

P(-3)=0

1, - 1, - 3 are the zeros of cubic polynomial x cube + 3 x square minus x minus 3

relationship between zeros and the coefficients

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

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

Sum and product of zeroes taken at a time

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

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