Multiple choice

What will be quadratic equation in $x$, when the roots have arithmetic mean $A$ and the geometric mean $G $

  1. $x^2 +2Ax+G^2 =0$
  2. $x^2 +G^2x +A =0$
  3. $x^2 -2Ax+G^2=0$
  4. $x^2 +Gx +A =0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a quadratic equation x^2 - (sum of roots)x + (product of roots) = 0, the sum of roots is 2 * (arithmetic mean) = 2A, and the product of roots is (geometric mean)^2 = G^2. Substituting these gives x^2 - 2Ax + G^2 = 0.

AI explanation

For a quadratic equation $x^2 - Sx + P = 0$, the coefficients depend on the sum $S$ and the product $P$ of its roots. The arithmetic mean $A$ represents half the sum of the roots, meaning the sum $S = 2A$. The geometric mean $G$ represents the square root of the product of the roots, meaning the product $P = G^2$. Substituting these values into the standard form of a quadratic equation gives the result $x^2 - 2Ax + G^2 = 0$.

Keep practicing — related questions