Question

If a and b are distinct real numbers, show that the quadratic equation

$2(a {}^{2} + b {}^{2} )x {}^{2} + 2(a + b)x + 1 = 0 \\ \\ has \: \:no \: \: real \: \: roots.$

Answer 1

discriminant
= 4( a+b)^2 -8(a^2 + b^2)

4 a^2+ 4 b^2 +8 ab - 8 a^2 - 8 b^2

- 4 a^2 - 4b^2 + 8 ab

- ( 2a -2b)^2 <0

So it has no real roots