Question

discuss the nature of the roots :$x^2 - ( p+1 )x + p = 0$

Answer 1

Step-by-step explanation:

The discriminant of a quadratic equation 

ax2+bx+c=0 is given by b2−4ac

a=2,b=2(p+1) and c=p

[2(p+1)]2−4(2p)⇒4(p+1)2−8p

⇒4[(p+1)2−2p]⇒4[(p2+2p+1)−2p]

⇒4(p2+1)

For any real value of p,4(p2+1) will always be positive as p2 cannot be negative for real p.

Hence, the discriminant b2−4ac will always be positive. 

When the discriminant is greater than 0 or is positive, then the roots of a quadratic equation will be real.