Question

Verify that the numbers given along side of the cubic polynomial below are their zeros.Also verify the relationship between the zeros and coefficients in each case: (i) f(x)=2x^(3)+x^(2)-5x+2;
(1)/(2) , 1 , -2​

Answer 1

f(x) =2x^3+x^2-5x+2

f(1/2)=2(1/2)^3+(1/2)^2-5(1/2)+2

f(1/2)=2(1/8)+1/4-5/2+2

f(1/2)=1/4+1/4-5/2+2

f(1/2)=2/4-5/2+2

f(1/2)=(1×2)-(2×5)/4+2

f(1/2)=2-10/4+2

f(1/2)=-8/4+2

f(1/2)=-2+2

f(1/2)=0

f(1)=2(1)^3+(1)^2-5(1)+2

f(1)=2(1)+1-5(1)+2

f(1)=2+1-5+2

f(1)=3-5+2

f(1)=-2+2

f(1)=0

f(-2)=2(-2)^3+(-2)^2-5(-2)+2

f(-2)=2(-8)+4+10+2

f(-2)=-16+4+10+2

f(-2)=-12+10+2

f(-2)=-2+2

f(-2)=0

(1)/(2) , 1 , -2 are the zeroes of the cubic polynomial f(x)=2x^(3)+x^(2)-5x+2

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 a time

=Coefficient of x/coefficient of x^3=-5/2

I hope it's help you

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