If the A.M. and G.M. of the roots of a quadratic equation in $x$ are $\mathrm{p}$ and q respectively, then…

If the A.M. and G.M. of the roots of a quadratic equation in $x$ are $\mathrm{p}$ and q respectively, then its equation is
  1. $x^{2}+2 p x+q^{2}=0$
  2. $x^{2}+p x+q^{2}=0$
  3. $x^{2}-p x+q^{2}=0$
  4. $x^{2}-2 p x+q^{2}=0$

Solution

$v^{\prime}=2 v$ $\frac{x_{1}+x_{2}}{2}=p \quad \& \quad \sqrt{x_{1} x_{2}}=q$ None $a x^{2}+b x+c=0$ $b=-\left(x_{1}+x_{2}\right)$ $c=x_{1} x_{2}$ $b=-2 p$ $\therefore r q^{n}=x^{2}-2 p x+q^{2}=0$

Asked in: MHT CET 2020 (15 Oct Shift 2)

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