Art, asked by mewtwokabadla93, 8 months ago

If the roots of the equation (a + b)2 + 2 (bc-ad)x+2+ = 0 are equal, show that a + bd = 0.​

Answers

Answered by Anonymous
1

Answer:

ac + bd = 0

Step-by-step explanation:

Given

,Roots of (a²+b²)x²+2(bc-ad)x+c²+d²=0 are equal, which means discriminant is 0.= > discriminant = 0

= > [ 2( bc - ad ) ]² - 4( a² + b² )( c² + d² ) = 0

= > [ 4( bc - ad )² ] - 4[ a²c² + a²d² + b²c² + b²d² ] = 0

= > 4[ ( b²c² + a²d² - 2abcd ) - ( a²c² + a²d² + b²c² + b²d² ) ] = 0

= > [ b²c² + a²d² - 2abcd - a²c² - a²d² - b²c² - b²d²] = 0

= > [ - 2abcd - a²c² - b²d² ] = 0

= > a²c² + b²d² + 2ac.bd = 0

= > ( ac + bd )² = 0

= > ac + bd = 0

Hence proved.

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