Embibe Experts Solutions for Chapter: Quadratic Equations, Exercise 1: Exercise

Divit has a field with total area of $1260 {\mathrm{m}}^2$. He uses this field to grow wheat and rice. The land used to grow wheat i.e. wheat land is rectangular in shape while the rice land is in the shape of a square. Length of wheat land is found to be $3 \mathrm{m}$ more than twice the length of the rice land.

The ratio of area of wheat land to the rice land is?

Aditya and Deepika went to Varanasi during their holidays. Deepika wanted to visit all the ghats of Varanasi. So, they hired a motor boat for this purpose. While riding, Aditya observed that the speed of motor boat was $20 \mathrm{km}/\mathrm{h}$. He was curious to know the speed of river Ganga. So, he noted the time taken by the boat to travel upstream and downstream in the river. He noticed that the boat took $1$ hour more to travel upstream than downstream to cover a distance of $15 \mathrm{km}$.

What is the time taken by the boat to travel the distance downstream?

The diagram shows the graph of the function $y=A{x}^2+Bx+C$.

Complete the table below to show whether each expression is positive, negative or zero.

$\begin{array}{|llll|}\hline \text{ Expression }& \text{ positive }& \text{ negative }& \text{ zero }\\ A& & & \\ C& & & \\ B^2-4AC& & & \\ B& & & \\ \hline\end{array}$

$\frac{1}{\left(x-1\right)\left(x-2\right)}+\frac{{\displaystyle 1}}{{\displaystyle \left(x-2\right)\left(x-3\right)}}=\frac{2}{3}$

A chess board contains $64$ equal squares and the area of each square is $25 {\mathrm{cm}}^2$. A border around the board is $2 \mathrm{cm}$ wide. Find the length of the side of the chess board.

Form a quadratic equation whose roots are $\frac{3+\sqrt{5}}{2}$ and $\frac{3-\sqrt{5}}{2}$.

Show that, if the roots of the following quadratic equation are equal, then $ad=bc$

$x^2\left(a^2+b^2\right)+2\left(ac+bd\right)x+\left(c^2+d^2\right)=0$

A motor boat whose speed is $18 \mathrm{km}/\mathrm{h}$ in still water takes $1$ hour more to go $24 \mathrm{km}$ upstream than to return downstream to the same spot. Find the speed of the stream.