Question

if the equation (a²+b²)x²-2b(a+c)x+b²+c²=0 has equal root then​

Answer 1

Answer:

The roots of the equation (a² + b²)x² - 2b(a + c)x + (b² + c²) = 0 are equal. here in question, the roots of equation are equal. Therefore the option (b) b² = ac, is correct choice.

Answer 2

CORRECT QUESTION.

If the roots of equation

( a² + b² ) x² - 2b ( a + c) x + ( b² + c² ) = 0

are equal then a, b, c are in

EXPLANATION.

The roots of equation =>

=> ( a² + b² ) x² - 2b ( a + c) x + ( b² + c² ) = 0

Therefore,

=> D = 0

=> b² - 4ac = 0

=> 4b² ( a+ c )² = 4 ( a² + b² ) ( b² + c² )

=> b² [ a² + c² + 2ac ] = [ a²b² + a²c² + b⁴ + b²c²]

=> b²a² + b²c² + 2ab²c = a²b² + a²c² + b⁴ + b²c²

=> b⁴ - 2ab²c + a²c² = 0

=> ( b² - ac )² = 0

=> b² = ac

Therefore,

a, b, c are in G. p