Question

Show that the equation $2(a^2+b^2)x^2+2(a+b)x+1=0$ has no real roots, when $a\ne b.$

Answer 1

For an equation the nature of the roots can be determined by the value of D.
where D =
If,
D > 0, real and unequal roots
D=0 , real and equal roots
D<0 , real roots don't exist

Here,
D=

Since D <0, no real roots exist.