Section: D (4 marks each)23,0btain all other zeros of the polynomial 3

1.	Section: D (4 marks each)23,0btain all other zeros of the polynomial 3x4 + 6x3-2x2-10x-5,if twoof its zeros are.and-li
Answer» p(x)=3x4+6x3-2x2-10x-5 as we have given that two of its zeroes are √(5/3) and -√(5/3). so their factors are; (x-√(5/3)) and (x+√(5/3)). the product of the factors ; (x-√5/3) (x+√5/3)=x^2-5/3 =3x^2-5/3=1/3(3x^2-5) where k=1/3 now g(x)=3x^2-5 dividing p(x) by g(x) we get q(x)=x^2+2x+1 by division algorithm; p(x)=g(x)*q(x)+r(x) =(3x^2-5)(x^2+2x+1) =(3x^2-5)(x^2+x+x+1) =(3x^2-5)(x(x+1)+1(x+1) (3x^2-5)(x+1)(x+1) the other two zeroes are -1 and-1

Section: D (4 marks each)23,0btain all other zeros of the polynomial 3x4 + 6x3-2x2-10x-5,if twoof its zeros are.and-li

Answer»

p(x)=3x4+6x3-2x2-10x-5

as we have given that two of its zeroes are √(5/3) and -√(5/3). so their factors are;

(x-√(5/3)) and (x+√(5/3)). the product of the factors ;

(x-√5/3) (x+√5/3)=x^2-5/3

=3x^2-5/3=1/3(3x^2-5)

where k=1/3

now g(x)=3x^2-5

dividing p(x) by g(x) we get

q(x)=x^2+2x+1

by division algorithm;

p(x)=g(x)*q(x)+r(x)

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

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

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

(3x^2-5)(x+1)(x+1)

the other two zeroes are -1 and-1