KVPY2010MathematicsQuadratic Equation
The roots of (x-41)⁴⁹+(x-49)⁴¹+(x-2009)²⁰⁰⁹=0 are -
Options
- Aall necessarily real
- Bnon-real except one positive real root
- Cnon-real except three positive real roots
- Dnon-real except for three real roots of which exactly one is positive
Correct answer
B. non-real except one positive real root
Step-by-step solution
array l (x-41)⁴⁹+(x-49)⁴¹+(x-2009)²⁰⁰⁹=0 f(x)=(x-41)⁴⁹+(x-49)⁴¹+(x-2009)²⁰⁰⁹ f^ (x)=49(x-41)⁴³+41(x-49)⁴⁰+2009(x-2009)⁴⁸>0 array hence f ( x ) will cut x -axis only once. 1 real root.