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# What are the zeroes of f(x) = x^{2} + 5x + 6?

x = -2, -3

x = 2, 3

x = -2, 3

x = 2, -3

**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 x^{2 }= 1,

b is the coefficient of x which is 5 and c is the constant term = 6.

**Step 2: **

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

1 × (6) = 6

**⇒ 3 and 2 are the factors that add up to b.**

**Step 3:**

Split 5x into two terms.

x^{2} + 3x + 2x + 6 = 0

**Step 4: **

**Take out the common factors by grouping.**

x(x + 3) + 2 (x + 3) = 0

(x + 3) (x + 2) = 0

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

x + 3 = 0 and x + 2 = 0

x = - 3 and x = - 2

**Thus, the two values that satisfy the equation are - 3 and - 2.**

## What are the zeroes of f(x) = x^{2} + 5x + 6?

x = -2, -3, x = 2, 3, x = -2, 3 x = 2, -3

**Summary:**

The zeroes of f(x) = x^{2} + 5x + 6 are x = -3, -2 which satisfies the equation.

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