Question

If ad is not equal to dc then prove that the equation (a²+b²)xx+2(ac+bd)x+(c²+d²)=0 has no real roots

Answer 1

(a²+b²)x²+2(ac+bd)x+(c²+d²)=0
a=(a²+b²)  b=2(ac+bd)  c=(c²+d²)
putting a,b,c in formula
[-b +/- √(b²-4ac)]/2a
{-2(ac+bd) +/-√[4(ac+bd)²-4(a²+b²)(c²+d²)]}/2(a²+b²)
[-2(ac+bd) +/- √4a²c²+4b²d²+8abcd-4a²c²-4a²d²-4b²c²-4b²d²]/2(a²+b²)
-2(ac+bd) +/- √ - (4a²d²-8abcd+4b²c²)
Hence root cant be negative.
So, it has no real roots.

Answer 2

Answer:

Step-by-step explanation

I have attached a pic representing the answer guys