Find the nature of roots of $$2(p+q)²x² +2(p+q)x + 1 = 0$$​​

Correct option is B

Given:

Given quadratic equation $$2(p+q)²x² +2(p+q)x + 1 = 0$$​​

Formula Used:

Determinant D =$$b^2 - 4ac$$​​

If D > 0 then roots are real and distinct

If D = 0 then roots real and equal

If D<0 then roots are imaginary

Solution:

For the equation $$2(p+q)²x² +2(p+q)x + 1 = 0$$​​

$$D = (2(p+q))^2 - 4(2(p+q)^2)(1)\\ \ \\ =4(p+q)^2 - 8(p+q)^2\\ \ \\ = -4(p+q)^2$$​

So $$-4(p+q)^2 < 0$$       [Negative values are less than zero]

The roots are imaginary

So correct option is (b)