If 2 is a root of the equation $$x^2 -px +6 = 0$$​ and the quadratic equation $$x^2 +2px + q = 0$$ has equal roots, then the value of q is:

Correct option is A

Given:

Roots of quadratic equation $$x^2 -px +6 = 0$$​ is 2

Quadratic equation $$x^2 +2px + q = 0$$​ has equal roots

Formula Used:

For a quadratic equation $$ax^2 + bx + c = 0$$​​

If roots are equal then discriminant $$D = b^2 - 4ac = 0$$​​

Solution:

Putting the value of x in $$x^2 -px +6 = 0$$​​

​$$(2)^2 -p(2) +6 =0$$​​

4 - 2p + 6 = 0

2p =10

p = 5

​$$x^2 +2px + q=0$$​has equal roots

Then D $$= (2p)^2 - 4(1)(q)=0$$​​

​$$(10)^2- 4q=0$$​​

4q = 100

q= 25