2022 · Q25
How many of the following values of x would satisfy the equation qx² - 2px + q = 0?1. x = (√(p+q)+√(p-q))/(√(p+q)-√(p-q)), where p > q2. x = (p+√(p²-q²))/(q), where p > q3. x = (√(p+q))/(√(p-q)), where p > qSelect the correct answer using the code given below :
Elementary MathematicsAlgebra
- AOnly one value
- BOnly two values
- CAll three values
- DNone
Explanation
The roots of qx²−2px+q = 0 are [p±√(p²−q²)]/q. Value 2 is the '+' root. Value 1 rationalises to (2p+2√(p²−q²))/(2q), the same '+' root. Value 3 equals √((p+q)/(p−q)); e.g. p=5,q=3 gives 2 while the actual roots are 3 and 1/3. Hence exactly two of the values satisfy the equation, and the keyed option is B.