(a²+b²)x²-2(ac+bd)x+(c²+d²)=0 দ্বিঘাত সমীকরণের বীজদ্বয় সমান হলে, প্রমাণ করি যে,a/b=c/d
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The given quadratic equation is (a2 + b²)x2 -2(ac + bd)x + (c² + d²) = 0.
If the roots of given quadratic equation are equal, then its discriminant is zero.
.:. D = [−2(ac + bd)²] − 4(
⇒ 4(a²c² + b²d² + 2abcd) —
-
⇒ 4(a²c² + b²d² + 2abcd
⇒2abcd-a²d²b²c² = 0
⇒a²d² + b²c² - 2abcd = 0
⇒ (ad - bc)² = 0
⇒ ad-bc = 0
→ ad = bc
C d a b ←
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