What are the zeroes of f(x) = x² + 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 x² = 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.

x² + 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.

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What are the zeroes of f(x) = x² + 5x + 6?
x = -2, -3, x = 2, 3, x = -2, 3 x = 2, -3

Summary:

The zeroes of f(x) = x² + 5x + 6 are x = -3, -2 which satisfies the equation.