Question

find all the zeros of 2 x cube + x square - 6 x minus 3 if two of its zeros are under root 3 and minus under root 3​

Answer 1

Answer:

The zeroes of given polynomial = $\sf{ \dfrac{-1}{2}}$

Given:-

• two zeros are √3 and -√3

To find:-

• All the zeroes of the polynomial

Solution:-

$\sf\boxed{2x^3 + x^2 - 6x -3}$

Therefore, x = √3 is a zero, x - √3 is a factor

and x = -3 is a zero, x + √3 is a factor

Hence, (x + √3)(x - √3) is also a factor

$\implies \sf{x^2 - ( \sqrt{3})^2}$

$\implies \sf{x^2 - 3}$

For finding other zero, we divide the given polynomial by (x² - 3)

Therefore, $\sf{2x^3 + x^2 - 6x -3 = (x^2 - 3)(2x + 1)}$

Hence, $\sf{(x^2 - 3)(2x + 1) = 0}$

$\implies \sf{2x = -1}$

$\implies \sf{x = \dfrac{-1}{2}}$

Therefore, zeroes of the given polynomial are $\sf{ \dfrac{-1}{2} , \sqrt{3} , - \sqrt{3}}$

$\rule{200}{2}$