If ad $\ne$ bc, then prove that the equation (a 2 + b 2 )x 2 + 2(ac + bd)x + (c 2 + d 2 ) = 0 has no real roots.

If ad $\ne$ bc, then prove that the equation

If ad $\ne$ bc, then prove that the equation

(a² + b²)x² + 2(ac + bd)x + (c² + d²) = 0 has no real roots.

D = 4(ac + bd)² - 4(a² + b²)(c² + d²)

= -4(a²d² + b²c² - 2abcd)

= -4(ad - bc)²

Since ad $\ne$ bc

Therefore D < 0

The equation has no real roots.