Question

Prove that the equation x^2(a^2+b^2) +2 x( ac+bd)+c^2+d^2)=0 has no real roots , ad¥ bc Write the answer fast then I will mark you brainliest .

Answer 1

Step-by-step explanation:

Just find its discriminant using the formula b^2-4ac , if it is less than 0 , then you can infer that this equation has no real roots

Answer 2

Answer :

Explanation :

Solution :

Let D be the discriminant of the equation (a^2+ b ^2)x^2 +2x (ac+bd)+ c^2 + d^2 = 0

Then , D = 4 (ac+bd)^2 - 4 ( a^2+b^2)(c ^2+ d ^2 ) =0 .

D = 4 [(ac+bd)^2 - 4 (a^2 + b^2)(c^2 + d^2 )]

D = 4 [ a^2c^2 + b^2 d^2 +2ac×bd - a^2c^2 - a^2d^2 - b^2c^2 - b^2d^2 ]

D = 4 [ 2ac × bd - a^2d^2 - b^2c^2 ]

= - 4 [ a^2 d^2 + b^2 -2ad ×bc ]

= - 4 ( ad- bc )^2

It is given that ad not = to bc

=> ad - bc not= to 0

=> ( ad - bc )^2 > 0

=> -4 ( ad - bc ) ^2 < 0

=> D <0

Hence , the given equation has no real roots .

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