Question

(a²-b²-c²+d²)²-4(ad-bc)²

full explanation​

Answer 1

Answer:

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Step-by-step explanation:

According to question, the given equation is

x2(a2 + b2)+ 2x (ac + bd) +(c2 + d2)= 0 .

Let D be the discriminant of this equation.

Therefore,D = 4(ac + bd)2 - 4(a2 + b2)(c2 + d2)

⇒ D = 4 [(ac+ bd)2 - (a2 + b2) (c2 + d2)]

⇒ D = 4 [a2c2 + b2d2 + 2ac.bd - a2c2 - a2d2 - b2c2 - b2d2]

⇒D = 4 [2ac.bd - a2d2 - b2c2] = - 4[a2d2 + b2c2 - 2ad.bc] = -4(ad - bc)2

It is given that ad ≠ bc.

⇒ ad - bc ≠ 0

⇒ (ad - bc)2 > 0

⇒ - 4 (ad - bc)2 < 0

⇒ D < 0.

Therefore, given equation has no real root.

Answer 2

Step-by-step explanation:

Answer:

make me branalist please

Step-by-step explanation:

According to question, the given equation is

x2(a2 + b2)+ 2x (ac + bd) +(c2 + d2)= 0 .

Let D be the discriminant of this equation.

Therefore,D = 4(ac + bd)2 - 4(a2 + b2)(c2 + d2)

⇒ D = 4 [(ac+ bd)2 - (a2 + b2) (c2 + d2)]

⇒ D = 4 [a2c2 + b2d2 + 2ac.bd - a2c2 - a2d2 - b2c2 - b2d2]

⇒D = 4 [2ac.bd - a2d2 - b2c2] = - 4[a2d2 + b2c2 - 2ad.bc] = -4(ad - bc)2

It is given that ad ≠ bc.

⇒ ad - bc ≠ 0

⇒ (ad - bc)2 > 0

⇒ - 4 (ad - bc)2 < 0

⇒ D < 0.

Therefore, given equation has no real root.