​If 3 is a root of the equation $$x^2 - px + 15 = 0$$ and the quadratic equation $$x^2 + px + q = 0$$ has equal roots, then the value of is: ​

Correct option is A

Given :

​$$x^2 - px + 15 = 0 \quad$$has root 3

​$$x^2 - px + q = 0 \quad$$has equal root 

Concept Used 

quadratic equation $$ax^2 +bx+c =0$$ 

for equal root the discriminant D = 0 

where $$D = b^2 -4ac$$​​

Solution :

​$$x^2 - px + 15 = 0 \quad$$​​

​Here, $3$ is a root, so substitute $x=3$ into the equation:

9 - 3p + 15 = 0

p = 8 

Now, 

​$$x^2 - px + q = 0 \quad$$

put p = 8  

For the equation to have equal roots, the discriminant must be zero:

​​​Discriminant : $$p^2 - 4q = 0$$​​

64 - 4q = 0

q = 16

The correct answer is option (a) 16