Question
Fri November 18, 2011 By:
Expert Reply
Sat November 19, 2011
The question that you have typed has a mistake...in the second term it should be ac+bd and not ab+bd. if you will make that change then the answer will be  d) ad?bc
 
Now for the given quadratic equation to have no real roots 
this means that it has imaginary roots, so the discriminant must be
less than zero.
 
D<0
 
Now let us calculate the value of D
 
D=[2(ac+bd)]2-4(a2+b2)(c2+d2)
 
=4(a2c2+2abcd+b2d2-a2c2-a2d2-b2c2-b2d2)
 
=4(2abcd-a2d2-b2c2)
 
=-4(-2abcd+a2d2+b2c2)
 
D=-4(ad-bc)2
 
Now this D will be always negative since the perfect square will be always positive and
negative sign outside makes the whole expression negative provided the square term
is not zero.
 
Hence ad-bc?0
 
So,  ad?bc
 
So, if ad is not equal to bc
the D will be always negative and hence no real soultions.
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