Question

Find a cubic function with the given zeros. Square root of six., - Square root of six., -3

Answer 1

Let f(x) be the cubic polynomial with the given zeroes.

The zeroes are $x_1=\sqrt{6}$, $x_2=-\sqrt{6}$ and $x_3=-3$

Thus, the f(x) will be:

$f(x)=(x-x_1)(x-x_2)(x-x_3)$

Therefore, we have:

$f(x)=(x-\sqrt{6})(x-(-\sqrt{6}))(x-(-3))=(x-\sqrt{6} )(x+\sqrt{6})(x+3)$

$\therefore f(x)=(x^2-6)(x+3)=x^3-3x^2-6x-18$ This is the required cubic function with the given zeros.

Answer 2

As per the question, it is a cubic function, let’s say, f(x, y, z) and the roots are square root of 6, - square root of 6 and -3 which can be represented as,

x – square root of 6

x – (- square root of 6) = x + square root of 6

x – (-3) = x + 3

Hence, to determine the function all you need to do is multiply the roots,

F (x) = (x – square root of 6) (x + square root of 6) (x + 3)