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If the roots of Equation (a^2+b^2)x^2-2(ac+bd)x+(c^2+d^2)=0 …

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If the roots of Equation (a^2+b^2)x^2-2(ac+bd)x+(c^2+d^2)=0 are equal. Then prove that a/b=c/d or ad-bc=0

Posted by Samraat Sahil Verma 5 years, 2 months ago

CBSE > Class 10 > Mathematics

3 answers

? Yang ? 5 years, 2 months ago

Here, A = (a² + b²), B = - 2(ac + bc) and C = (c² + d²). As roots are equal, D ⇒ b² - 4ac = 0 B² = 4ac ⇒ [- 2(ac + bd)]² = 4(a² + b²) (c² + d²) ⇒ (a²c² + 2abcd + b²d²) = 4(a²c² + a²d² + b²c² + b²d²) ⇒ 2 abcd = a²d² + b²c² ⇒ 0 = a²d² - 2abcd + b²c² ⇒ 0 = (ad - bc)² ⇒ 0 = ad - bc ⇒ ad = bc ⇒ a/b = c/d. HOPE IT HELPS YOU?✌

Rohit Kumar 5 years, 2 months ago

Answer :- Here, A = (a² + b²), B = - 2(ac + bc) and C = (c² + d²) As roots are equal, D ⇒ b² - 4ac = 0 B² = 4ac ⇒ [- 2(ac + bd)]² = 4(a² + b²) (c² + d²) ⇒ (a²c² + 2abcd + b²d²) = 4(a²c² + a²d² + b²c² + b²d²) ⇒ 2 abcd = a²d² + b²c² ⇒ 0 = a²d² - 2abcd + b²c² ⇒ 0 = (ad - bc)² ⇒ 0 = ad - bc ⇒ ad = bc ⇒ a/b = c/d

Riya Philip 5 years, 2 months ago

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