Question

If (a² + b²) x² + 2 (ac + bd) x + c² + d² = 0 has no real roots, then
A. ad = bc
B. ab = cd
C. ac = bd
D. ad ≠ bc

Answer 1

D. ad ≠ bc

Step-by-step explanation:

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

d = b² - 4ac

  = 4(ac + bd)² - 4(a²+b²)(c²+d²)

  =4(a²c² +b²d² -abcd) -4(a²c² + b²d² + a²d² + b²c²)

  = -4(a²d² +b²c² - 2abcd)

  = -4(ad - bc)²

D is less than zero, a negative. So ad ≠ bc.

Option D is the answer.