Given:
The product of a particular number is 65.
Second value is given by the sum of 8 and the original number.
To find:
The unknown number.
Solution:
Let x be the unknown number.
Then, second number = x+8
The product of a particular number is 65.
[tex]x\times (x+8)=65[/tex]
[tex]x^2+8x=65[/tex]
[tex]x^2+8x-65=0[/tex]
Splitting the middle term, we get
[tex]x^2+13x-5x-65=0[/tex]
[tex]x(x+13)-5(x+13)=0[/tex]
[tex](x-5)(x+13)=0[/tex]
Using zero product property, we get
[tex]x-5=0[/tex] and [tex]x+13=0[/tex]
[tex]x=5[/tex] and [tex]x=-13[/tex]
So, the unknown number is either 5 or -13.
Therefore, the correct option is B.
