How do you solve #-5x^2 + 10x + 15 = 0#?

1 Answer
Jun 18, 2016

Answer:

#x=-1 or x=3#

Explanation:

#-5x^2+10x+15=0#
#=-5(x^2-2x-3)=0#
To factorize the polynomial #x^2-2x-3# in the form #(x+a)(x+b)#
we have to find two integers #a# and #b# such that
#a+b=-2# and #a*b=-3#

check for #a=1# and #b=-3#
so,#color(blue)((x^2-2x-3)=(x+1)(x-3))#

#-5x^2+10x+15=0#
#rArr-5(x+1)(x-3)=0#

Knowing that if the product is zero then one of the factors can be equal to zero .

Since #-5!=0#
Therefore,

#x+1=0#
#x=-1#

Or,
#x-3=0#
#x=3#