Question

যদি ax²+ bx+c= 0, দ্বিঘাত সমীকরণের বীজদ্বয়ের অনুপাত 1: r হয়, তবে, দেখাও যে(r+1)²/r=b²/ac​

Answer 1

Given :

ax² + bx + c = 0,

the ratio of the two seeds of the quadratic equation is 1: r,  

To Find : show that (r + 1) ² / r = b² / ac

Solution :

Roots are α , αr

Sum of roots = α + αr   = - b/a

=> r + 1 = -b/aα

=> r  + 1 =    -b/aα  

Product of roots = α.αR   = c/a

=> r = c/aα²

(r + 1) ² / r = b² / ac

LHS =  (r + 1) ² / r

= ( -b/aα)² / (c/aα²)

= (b²/a²)/(c/a)

= b²/ac

= RHS

QED

(r + 1) ² / r = b² / ac

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