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

Quadratic Equations (10)

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

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

Answer

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.

Exam Year: 2017