Question

The roots of the equation x² + x − (a + 1) (a +2) = 0 are ______.

Options

• (a + 2), − (a + 1)

• −(a + 2) (a + 1)

• (a + 2), (a + 1)

• −(a + 2), − (a + 1)

Answer 1

The roots of the equation x² + x − (a + 1) (a +2) = 0 are −(a + 2) (a + 1).

Explanation:

Given:

x² + x − (a + 1) (a + 2) = 0

(a + 1) (a + 2) = a² + 3a + 2

x² + x − (a² + 3a + 2) = 0

x² + x − a² − 3a − 2 = 0

We look for two numbers whose product is −(a + 1) (a + 2) and whose sum is 1.

(x + a + 2) (x − a − 1) = 0

x + a + 2 = 0 or x − a − 1 = 0

x = −(a + 2) or x = a + 1

The roots of the equation are:

a + 1 and −(a + 2)​