Question

1.Show that if the roots of the equation
$( {a}^{2} + {b}^{2} ) {x}^{2} + 2(bc + ad)x + ( {c}^{2} + {d}^{2} ) = 0$
are real then they must be equal.​

Answer 1

Answer:

a2+b2)x2−2(ac+bd)x+(c2+d2)=0 has equal roots.

Therefore, discriminant =0

Thus [2(ac+bd)]2+4(a2+b2)(c2+d2)

⇒a2c2+b2d2+2ac.bd=a2c2+a2d2+b2c2+b2d2

⇒(ad−bc)2=0$

⇒ad−bc=0

⇒ad=bc

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Answer 2

Question:-

Show that if the roots of the equation

$( {a}^{2} + {b}^{2} ) {x}^{2} + 2(bc + ad)x + ( {c}^{2} + {d}^{2} ) = 0$

are real then they must be equal.

Solution:-

Refer To Attachment