NDA2010MathematicsQuadratic EquationActual
If the roots of the equation (a^2+b^2 ) x^2-2 b(a+c) x+ (b^2+c^2 )=0 are equal, then which one of the following is correct?
Options
- A2 b=a+c
- Bb^2=a c
- Cb+c=2 a
- Db=a c
Correct answer
B. b^2=a c
Step-by-step solution
Since roots of the equation are equal then b^2-4 a c=0 i.e., 4 b^2(a+c)^2-4 (a^2+b^2 ) (b^2+c^2 )=0 b^2 (a^2+2 a c+c^2 )- (a^2 b^2+a^2 c^2+b^4+b^2 c^2 )=0 a^2 b^2+2 a b^2 c+b^2 c^2-a^2 b^2-a^2 c^2-b^4-b^2 c^2=0 2 a b^2 c-a^2 c^2-b^4=0 b^4-2 a b^2 c+a^2 c^2=0 (b^2-a c )^2=0 b^2=a c .