If the roots of quadratic equation$$(2-p)x^2+2px-(p+1)=0$$​ are equal, then the value of p is:

Correct option is B

Given:

Equation

​$$(2-p)x^2+2px-(p+1)=0$$

Concept Used:

The discriminant Δ for a quadratic equation    $$ax 2 ​+ b x + c = 0$$  is  given by:

$$Δ = b 2 − 4 a c$$

For the roots to be equal, the discriminant must be zero: $$\Delta = 0$$​​

Solution:

From the Equation 

$$(2-p)x^2+2px-(p+1)=0$$​

​Substitute the values of a , b and c , then discriminant

​$$Δ=(2p) 2 ​−4(2−p)(−(p+1))$$

$$\Delta = 4p^2 + 4(2 - p)(p + 1)$$

$$\Delta = 4p^2 + 4(-p^2 + p + 2)$$

Δ = 4p + 8

As Δ = 0, So 4p = −8