Question

Verify that -5, 1/2, 3/4 are zeros of cubic polynomial 4x^3+20x^2+2x-3. also verify the relationship between zeros and the coefficients

Answer 1

P(x)=4x^3+20x^2+2x-3

P(-5)=4(-5)^3+20(-5)^2+2(-5)-3

P(-5)=4(-125)+20(25)+2(-5)-3

P(-5)=-500+500-10-3

P(-5)=13

P(x)=4x^3+20x^2+2x-3

P(1/2)=4(1/2)^3+20(1/2)^2+2(1/2)-3

P(1/2)=4(1/8)+20(1/4)+2/2-3

P(1/2)=4/8+20/4+1-3

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

P(1/2)=1/2+3

P(1/2)=1/2+3/1

P(1/2)=(1×1)+(2×3)/2

P(1/2)=1+6/2

P(1/2)=7/2

P(x)=4x^3+20x^2+2x-3

P(3/4)=4(3/4)^3+20(3/4)^2+2(3/4)-3

P(3/4)=4(27/64)+20(9/16)+2(3/4)-3

P(3/4)=108/64+180/16+6/4-3

P(3/4)=(1×108)+(4×180)/64+3/2-3

P(3/4)=108+720/64+3/2-3

P(3/4)=828/64+3/2-3

P(3/4)=(1×828)+(32×3)/64-3

P(3/4)=828+96/64-3/1

P(3/4)=924/64-3/1

P(3/4)=(1×924)-(64×3)/64

P(3/4)=924-192/64

P(3/4)=732/64

-5,1/2,3/4 are not the zeroes of the cubic polynomial P(x)=4x^3+20x^2+2x-3

Relationship between zeroes and coefficients

Sum of zeroes=-(coefficient of x^2)/coefficient of x^3=-20/4=-5

Product of zeroes=-(constant term)/coefficient of x^3=-(-3)/4=3/4

Sum and product of zeroes taken at a time

=Coefficient of x/coefficient of x^3=2/4=1/2

I hope it's help you

Plz mark my answer as a brainliest answer