Telangana Board Solutions for Chapter: Quadratic Equations, Exercise 10: Exercise

Find the nature of the roots of the following quadratic equation. If real roots exist, find them:

$2x^2-3x+5=0$

Find the nature of the roots of the following quadratic equation. If real roots exist, find them:

$3x^2-4\sqrt{3}x+4=0$

Find the nature of the roots of the following quadratic equation. If real roots exist, find them:

$2x^2-6x+3=0$

Find the values of $k$ for the following quadratic equation, so that they have two equal roots:

$2x^2+kx+3=0$

Find the values of $k$ for each of the following quadratic equations, so that they have two equal roots

$kx(x-2)+6=0(k\ne 0)$

Is it possible to design a rectangular mangrove whose length is twice its breadth, and the area is $800 {\mathrm{m}}^2$? If so, find its length and breadth.

The sum of the ages of two friends is $20$ years. Four years ago, the product of their ages in years was $48.$ Is the above situation possible? If so, determine their present ages

Is it possible to design a rectangular park of perimeter $80 \mathrm{m}$ and area $400 {\mathrm{m}}^2$? If so, find its length and breadth. Comment on your answer.