Find the zeroes of x² − $5x + 6$ .

Answer: The zeroes of the polynomial are $2$ and $3$ .

Step-by-step solution

Step 1: Set the polynomial to zero

To find the zeroes of the polynomial, we set the expression equal to 0, forming a quadratic equation.

Step 2: Factor the quadratic equation

We look for two numbers whose product is 6 and whose sum is $-5$ . The two numbers are $-2$ and $-3$ , so we split the middle term and factor as $(x - 2)(x - 3) = 0$ .

Step 3: Solve for x

By the zero product property, setting each factor to 0 gives $x = 2$ and $x = 3$ .

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Find the zeroes of x² − 5x+65x + 65x+6.

Step-by-step solution

Step 1: Set the polynomial to zero

Step 2: Factor the quadratic equation

Step 3: Solve for x

Find the zeroes of x² − $5x + 6$ .