Question

Write the quadratic equation, the arithmetic and geometric means of whose roots are A and G respectively.

Answer 1

Correct Answer - `x^(2)-2Ax+G^(2)=0`
Let the roots of the quadratic equation be `alpha` and `beta`.
Then, the equation is `x^(2)-(alpha+beta)x+alpha beta=0`.
`:. A=(alpha +beta)/2 rArr alpha+beta =2A`.
`G =sqrt(alpha beta)rArr alpha beta=G^(2)`.
Hence, the required equation is `x^(2)-2Ax+G^(2)=0`.