What are the zeroes of f (x) = x² - 2x - 3?
x = -3, 1
x = -3, -1
x = 3, 1
x = 3, -1

Solution:

The zeroes of the polynomial make the values of the whole polynomial equal to zero.

Let us factorise the polynomial to find the value of x by splitting the middle term.

Step 1:

Identify the values of a, b and c.

In the above equation, a is coefficient of x² = 1, b is the coefficient of x = -2 and c is the constant term = -3.

Step 2:

Multiply a and c and find the factors that add up to b.

1 × ( - 3) = - 3

⇒ -3 and 1 are the factors that add up to b.

Step 3:

Split bx into two terms.

x² - 3x + 1x - 3 = 0

Step 4:

Take out the common factors by grouping.

x (x - 3) + 1 (x - 3) = 0

(x - 3) (x + 1) = 0

By putting the factors equal to zero we get two values of x

x - 3 = 0 and x + 1 = 0

x = 3 and x = - 1

Thus, the two values that satisfy the equation are 3 and - 1.

---

What are the zeroes of f (x) = x² - 2x - 3? x = - 3, 1 x = - 3, - 1 x = 3, 1 x = 3, - 1

Summary:

The zeroes of the equation f (x) = x² - 2x - 3 are x = 3, - 1 which satisfies the equation.