If –2 is a root of the equation $$3x^2+px+2=0$$​, and $$7x^2+px+k=0$$​ has equal roots, then what is the value of $$k$$​?

Correct option is B

Given:

Roots of the equation $$3x^2+px+2 = 0$$​ is -2

​$$7x^2+px+k=0$$​ 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 $$3x^2 +px+2 = 0$$​​

​$$3(-2)^2 +p(-2)+2 =0$$​​

12-2p+2=0

2p =14

p=7

​$$7x^2+px+k=0$$​ has equal roots

Then D = $$(p)^2 - 4(7)(k)=0$$​​

​$$(7)^2- 28k=0$$​​

28k = 49

k=$$\frac{49}{28} = \frac{7}{4}$$​​