question_answer

Let two numbers have arithmetic mean 9 and geometric mean 4. Then, these numbers are the roots of the quadratic equation

A) \[{{x}^{2}}+18x+16=0\]

B) \[{{x}^{2}}-18x+16=0\]

C) \[{{x}^{2}}+18x-16=0\]

D) \[{{x}^{2}}+18x-16=0\]

Correct Answer: B

Solution :

If \[\alpha \] and \[\beta \] are the roots of an equation, then the equation will be Letandbe two numbers whose arithmetic mean is 9 and geometric mean is 4.                                        ...(i) and                                        ...(ii) Required equation is   [from Eqs. (i) and (ii)] NOTE If a and to are two numbers, then their arithmetic meanand geometric mean.