Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Write the Quadratic Equation the Arithmetic and Geometric Means of Whose Roots Are Aand G Respectively. - Mathematics

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

#### Solution

$\text{ Let the roots of the required quadratic equation be a and b } .$
$\therefore A = \frac{a + b}{2} and G = \sqrt{ab}$
$\text{ The equation having a and b as its roots is }$
$x^2 - x\left( a + b \right) + ab = 0$
$\Rightarrow x^2 - 2Ax + G^2 = 0 \left[ \because A = \frac{a + b}{2} \text{ and } G = \sqrt{ab} \right]$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 20 Geometric Progression
Q 8 | Page 56