Question

obtain all the zeros of 2x3+x2-6x-3 if two of its zeros are root3&root-3

Answer 1

The zeroes are √3 , -√3 , and -1/2

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Answer 2

Answer:

Zeros of the given polynomial are $-\frac{1}{2},\sqrt3,-\sqrt3$

Step-by-step explanation:

Two zeros of the polynomial $2x^3+x^2-6x-3$are$\sqrt3,-\sqrt3$

If a and b are zeros of a polynomial then (x-a)(x-b) must be the factor.

Therefore, the factors are

$(x-\sqrt3)(x+\sqrt3)$

On applying the difference of squares formula  $(a+b)(a-b)=a^2-b^2$

$(x-\sqrt3)(x+\sqrt3)\\\\=x^2-(\sqrt3)^2\\\\x^2-3$

Now, for other zero, we divide the given polynomial by x^2-3

$\frac{2x^3+x^2-6x-3}{x^2-3}=2x+1$

Therefore, we have

$2x+1=0\\\\x=-\frac{1}{2}$

Therefore, zeros of the given polynomial are $-\frac{1}{2},\sqrt3,-\sqrt3$