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

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

2 Answers
May 10, 2018

x = -a or -b

Explanation:

As per the question, we hvae

x^2 + (a+b)x +ab = 0

:. x^2 + ax + bx + ab = 0

:. x(x + a) + b(x + a) = 0

:. (x + b)(x + a) = 0

:. x = -a or x = -b

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

May 10, 2018

color(blue)(x=-a)

color(blue)(x=-b)

Explanation:

x^2+(a+b)x+ab

Factor:

x^2+ax+bx+ab

x(x+a)+b(x+a)

[x(x+a)+b(x+a)]

(x+a)[x+b]

(x+a)(x+b)=0=>x=-a and x=-b