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Question

If the roots of the equation (a2+b2)x22(ac+bd)x+(c2+d2)=0 are equal, then abcd=

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Solution

we use this by using b24ac=4(ac+bd)24(a2+b2)(c2+d2)
= 4[(ac)2+2abcd+(bd)2]4((ac)2+(bc)2+(ac)2+(bd)2)
= 4(bc)2+8abcd4(ad)2
add 2abcd and 2abcd
we get
(bcad)2abcd=0
(bcad)=0
ad=bc
a/b=c/d
(a/b)(c/d)=0

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