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#