Question

HM between the roots of the equation $x^2-10x+11=0$ is

• A. $\frac{1}{5}$
• B. $\frac{5}{21}$
• C. $\frac{21}{20}$
• D. $\frac{11}{5}$

Answer 1

The correct option is D

$\frac{11}{5}$

Explanation for the correct option:

Let $p$ and $q$ be the roots of the equation $x^2-10x+11=0$.

Now,

Sum of roots is

$\begin{array}{rcl}p+q& =& -\frac{b}{a}\\ & =& 10\end{array}$

Product of roots is

$\begin{array}{rcl}pq& =& \frac{c}{a}\\ & =& 11\end{array}$

$\therefore$HM of $\left(p,q\right)=\frac{2pq}{(p+q)}$

$\begin{array}{rcl}& =& 2\left(\frac{11}{10}\right)\\ & =& \frac{22}{10}\\ & \mathbf{=}& \mathbf{}\frac{\mathbf{11}}{\mathbf{5}}\end{array}$

Hence option(D) is correct.