Question

17th one pls help fast

Answer 1

Answer:

Step-by-step explanation:

D = 4(ac+bd)^2 -4(a^2+b^2)(c^2+d^2)

=4(a^2c^2 + b^2d^2 + 2abcd) -4(a^2c^2 + a^2d^2 + b^2c^2 + b^2d^2)

=8abcd - 4a^2d^2 -4b^2c^2

= - (4a^2d^2 + 4b^2c^2 - 8abcd)

= - (2ad - 2bc)^2

for no real roots D < 0

=>  - (2ad - 2bc)^2 < 0

=>  (2ad - 2bc)^2 > 0

This will be always > 0  as square of any number is positive.

And D = 0 when 2ad = 2bc => ad = bc

Therefor, when ad and bc are not equal then no real roots