Question

What is the solution set for the quadratic function:

x² + 8x + 12 = 0

{2,6}
{12}
None
{-6, -2}

Answer 1

`\huge\boxed{\sf \{-6, -2\}}`

Explanation:

Given equation:

x² + 8x + 12 = 0

Using mid-term break formula.

• Break the mid-term (8x) into such two terms that the product of which gives the side terms and sum or difference of which gives the second terms.
• x² × 12 = 12x²
• Choose such two terms the product of which gives 12x².
• We can use 6x and 2x since 6x + 2x = 8x (mid-term) and 6x × 2x = 12x² (side-terms)

So, the equation becomes:

x² + 6x + 2x + 12 = 0

• Take common

x(x + 6) + 2(x + 6) = 0

• Now, take (x + 6) common

(x + 6)(x + 2) = 0

By zero's method:

x + 6 = 0 OR x + 2 = 0

So,

x = -6 OR x = -2

Solution set = {-6, -2}

`\rule[225]{225}{2}`