Paragraph: Let and be the roots of the equation x^2- (1-2 a^2 ) x+ (1-2 a^2 )=0 Question: Under what condition does the above equation have real roots?

Step-by-step solution

Using a x^2+b x+c=0a=1, b=- (1-2 a^2 ) & c= (1-2 a^2 ) For roots to be real, b ^2-4 ac 0 aligned & [- (1-2 a ^2 ) ]^2-4(1) (1-2 a ^2 ) 0 & 4 a ^4+4 a ^2-3 0 & (2 a ^2-1 ) (2 a ^2+3 ) 0 & a^2 1 2 or a^2 - 3 2 aligned