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

Question

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

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Answer 1 · 2018-05-10T08:42:10

#x = -a or -b#

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.

Answer 2 · 2018-05-10T09:09:25

#color(blue)(x=-a)#

#color(blue)(x=-b)#

#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#