Math, asked by dakshaldesai, 11 months ago

verify that 1, -2 and ½ arethe zero of 2x³-1x²-5x+2 .Also verify the relationship between zeros and
coefficient​

Answers

Answered by decentdileep
2

P(x)=2x³-1x²-5x+2

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

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

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

P(1)=-2

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

P(-2)=2(-8)-1(4)-5(-2)+2

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

P(-2)=-8

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

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

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

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

P(1/2)=-5/2+2/1

P(1/2)=(1×-5)+(2×2)/4

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

P(1/2)=-1/4

1,-2,1/2 are not the zeroes of the cubic polynomial 2x³-1x²-5x+2

Relationship between zeroes and coefficients

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

I hope it's help you

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