Math, asked by brainly73753, 11 months ago

for which condition, the quadratic equation (a² + b²) x² + 2 (b c – a d) x + (c² + d²) = 0 has real and equal roots?

...... plz ans...I have test today...so plz give correct ans...plz...​​

Answers

Answered by amishafilomeena1003
5

Answer:

.e. D = 0

= > b² - 4 ac = 0

From question we have given :

b = 2 ( b c - a d )

a = a² + b²

c = c² - d²

Now put all value in condition.

= > ( 2 ( b c - a d )² - 4 * ( a² + b² ) ( c² + d² ) = 0

= > 4 b² c² +4 a² d² - 8 b c a d - 4 * ( a² c² + a² d²+ b² c² + b² d² ) = 0

= >4 b² c² +4 a² d² - 8 b c a d - 4 a² c² - 4 a² d² - 4 b² c² - b² d² = 0

= > Clearly 4 b² c² & 4 a² d² cancel out .

= > - 8 b c a d - 4 a² c² - b² d² = 0

= > - 4 ( a² c² + b² d² + 2 a c b d ) = 0

= > ( a c + b d )² = 0

= > a c + b d = 0

Hence proved.

Step-by-step explanation:

hope this helps please follow

Answered by amishafilomeena1003
0

Answer:

.e. D = 0

= > b² - 4 ac = 0

From question we have given :

b = 2 ( b c - a d )

a = a² + b²

c = c² - d²

Now put all value in condition.

= > ( 2 ( b c - a d )² - 4 * ( a² + b² ) ( c² + d² ) = 0

= > 4 b² c² +4 a² d² - 8 b c a d - 4 * ( a² c² + a² d²+ b² c² + b² d² ) = 0

= >4 b² c² +4 a² d² - 8 b c a d - 4 a² c² - 4 a² d² - 4 b² c² - b² d² = 0

= > Clearly 4 b² c² & 4 a² d² cancel out .

= > - 8 b c a d - 4 a² c² - b² d² = 0

= > - 4 ( a² c² + b² d² + 2 a c b d ) = 0

= > ( a c + b d )² = 0

= > a c + b d = 0

Hence proved.

Step-by-step explanation:

hope this helps please follow

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