Question

Show that equation has no real roots :-
2(a^2+b^2) n^2+2(a+b)n+1=0

Answer 1

2(a² + b²)n² + 2(a + b)n + 1 = 0

Discriminant = {2(a + b)}² - 4.2(a² + b²)
= 4(a² + b² + 2ab ) -8(a² + b² )
= 4{ a² + b² + 2ab -2a² - 2b² }
= 4{2ab - a² - b² }
= - 4{ a² + b² -2ab }
= -4(a - b)²
hence, D = -4(a - b)² < 0 so, given polynomial have no real roots