Telangana Board Solutions for Chapter: Quadratic Equations, Exercise 11: Optional Exercise

Some points are plotted on a plane such that any three of them are noncollinear. Each point is joined with all remaining points by line segments. Find the number of points if the number of line segments are $10$.

A two-digit number is such that the product of its digits is $8$. When $18$ added to the number, they interchange their places. Determine the number.

A piece of wire $8\mathrm{m}$ in length is cut into two pieces, and each piece is bent into a square. Where should the cut in the wire be made if the sum of the areas of these squares is to be $2{\mathrm{m}}^2$.

Vinay and Praveen working together can paint the exterior of the house in $6$ days. Vinay by himself can complete the job in $5$ days less than Praveen. How long will it take Vinay to complete the job.

Show that the sum of roots of a quadratic equation ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0$ $(a\ne 0)$ is $\frac{-b}{a}$

Show that the product of roots of a quadratic equation ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0$ $(a\ne 0)$ is $\frac{c}{a}$

If the sum of the fraction and its reciprocal is $2\frac{16}{21}$, find the fraction.