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Question
Construct a quadratic in x such that A.M. of its roots is A and G.M. is G.
Solution
\[\text { Let the roots of the quadratic equation be a and b } . \]
\[ A = \frac{a + b}{2}\]
\[ \therefore a + b = 2A . . . . . . . . (i)\]
\[\text { Also, } G^2 = ab . . . . . . . (ii)\]
\[\text { The quadratic equation having roots a and b is given by } x^2 - (a + b)x + ab = 0 . \]
\[ \therefore x^2 - 2Ax + G^2 = 0 \left[ \text { Using (i) and (ii) } \right]\]
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