If 5 is one root of $$x^2 - (a - 1)x + 10 = 0$$​ , then the other root is:

Correct option is A

Given: ​

​$$x^2 - (a - 1)x + 10 = 0$$​ 

one root = 5 

Concept Used:  ​

Expression : ​$$ax^2 - bx + c = 0$$​  

Putting the value of the roots satisfies the condition of the roots.

Solution: ​

Putting the value of one of root = 5 

​$$x^2 - (a - 1)x + 10 = 0 \\ \ \\ (5)^2 -(a-1)5 +10 = 0 \\ \ \\ 25 -(a-1)5 + 10 = 0 \\ \ \\ -(a-1)5 = -10 -25 \\ \ \\ -(a-1)5 = -35 \\ \ \\ a-1 = 7 \\ \ \\ a = 8$$

Now, expression can be written as;

​$$x^2 -(8-1)x+10=0 \\ \ \\ x^2 -7x+10 =0 \\ \ \\ x^2 -5x-2x+10 = 0 \\ \ \\ x(x-5)-2(x-5) = 0 \\ \ \\ (x-2) (x-5) = 0$$ 

thus the roots are 2 and 5