$\"\"$ \ \

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 $\"\"$ .

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

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) \ \

$\"\"$ (Add and simplify) \ \

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

$\"\"$ and $\"\"$ (Simplify) \ \

There is five real roots are $\"\"$ , $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

$\"\"$

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