Question

if the roots of the equation ( a² + b²)x² +2( bc - ad )x + c² + d² = 0 are real and equal show that ac + bd = 0
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Answer 1

Answer:

Step-by-step explanation:

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Answer 2

The roots of the given equation are real and equal is,

$discriminate = 0$

So,

${(2(bc - ad))}^{2} - 4( {a}^{2} + {b}^{2} )( {c}^{2} + {d}^{2} ) = 0$

${bc}^{2} + {ad}^{2} - 2abcd - {ac}^{2} - {ad}^{2} - {bc}^{2} - {bd}^{2} = 0$

$- (ac + bd) ^{2} = 0$

So,

$ac + bd = 0.$