# How do solve x^2 + (a+b)x + ab =0?

## On my homework it simply says Solve the following quadratic equations:

May 10, 2018

$x = - a \mathmr{and} - b$

#### Explanation:

As per the question, we hvae

${x}^{2} + \left(a + b\right) x + a b = 0$

$\therefore {x}^{2} + a x + b x + a b = 0$

$\therefore x \left(x + a\right) + b \left(x + a\right) = 0$

$\therefore \left(x + b\right) \left(x + a\right) = 0$

$\therefore x = - a \mathmr{and} x = - b$

Hence, $x = - a , - b$ are the solution to this problem.

May 10, 2018

$\textcolor{b l u e}{x = - a}$

$\textcolor{b l u e}{x = - b}$

#### Explanation:

${x}^{2} + \left(a + b\right) x + a b$

Factor:

${x}^{2} + a x + b x + a b$

$x \left(x + a\right) + b \left(x + a\right)$

$\left[x \left(x + a\right) + b \left(x + a\right)\right]$

$\left(x + a\right) \left[x + b\right]$

$\left(x + a\right) \left(x + b\right) = 0 \implies x = - a \mathmr{and} x = - b$