Question

find the real value of p for which the equation x^2+ 2x + (p^2 + 1)=0 has real root​

Answer 1

Answer:

the given equation is:

x^2+2x+(p^2+1)=0

for real and roots;

=> D≥0

=> b^2 -4ac≥0

=> 2^2 -4•1•(p^2+1)≥0

=> 4-4(p^2+1)≥0

=> 1-(p^2+1)≥0

=> 1≥(p^2+1)

=> 0≥p^2

=> p^2≤0

∆case: (1)

when, p^2<0. ( neglected)

{ this is not possible, as p^2 is always positive and a positive real number can't be less then 0}

∆case:(2)

when,p^2=0

=> p=0

thus , the appropriate value of p is zero.

ie; p=0.

thank you