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
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.
Similar questions
Math,
4 months ago
Physics,
4 months ago
Computer Science,
8 months ago
History,
8 months ago
Math,
11 months ago