$\"\"$

The function is $\"\"$ .

If $\"\"$ is a rational zero, then $\"\"$ is a factor of $\"\"$ and $\"\"$ is a factor of $\"\"$ .

Here, $\"\"$ and $\"\"$ .

Write the possible value of $\"\"$ in simplest form.

$\"\"$ and $\"\"$ .

$\"\"$

Make a table and test some possible rational zeroes:

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

The depressed polynomial is $\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Observe the table:

Since $\"\"$ , there is a zero at $\"\"$ .

The depressed polynomial is $\"\"$ .

The quadratic function is $\"\"$ .

$\"\"$ (Quadratic formula)

$\"\"$ (Substitute $\"\"$ and $\"\"$ )

$\"\"$ (Simplify)

$\"\"$ (Subtract and simplify)

$\"\"$ and $\"\"$ (Separate two roots)

There is two irrational real roots are $\"\"$ and $\"\"$ , $\"\"$ and $\"\"$ .

$\"\"$

The zeroes of the functions are $\"\"$ and $\"\"$ .