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

A train travels a distance $1200 \mathrm{km}$ with a velocity $x \mathrm{km}/\mathrm{hr}$. If its velocity be $\left(x+10\right) \mathrm{km}$. Then it takes $10 \mathrm{hrs}$ less to cover the same distance. Then the value of $x$ is

The altitude of a triangle is $6 \mathrm{cm}$ more than its base. If its area is $108 {\mathrm{cm}}^2$, find the base and height of the triangle.

Akhil is an architect. He is into designing various villa projects. Akhil recently acquired $4$ acres of land to start a new villa project equipped with all necessary amenties. He decided to construct $10$ houses, each house occupying a land area of $25$ cents.

Akhil has designed small triangular-shaped parks in the plot for the kids to play. He also designed a beautiful garden in the middle of the plot. The park is designed such that the base of the triangular park is $8 \mathrm{m}$ less than twice its height. If the area of the triangle be $320 \mathrm{sq}.\mathrm{m}$, find its height.

Akhil is an architect. He is into designing various villa projects. Akhil recently acquired $4$ acres of land to start a new villa project equipped with all necessary amenties. He decided to construct $10$ houses, each house occupying a land area of $25$ cents. He also designed small triangular-shaped parks in the plot for the kids to play. He also designed beautiful gardens in the plot.

The perimeter of a rectangular and a square garden are both $160 \mathrm{metre}$. But the area of the square garden is $100 \mathrm{sq}.\mathrm{metre}$ more than the rectangular garden.The length and breadth of the rectangular garden are $?$

Amal and his family went for a trip to a resort. There are various amenities in the resort. He went for boating in the stream nearby the resort. There was a water tank near the stream to store water for gardening purposes in the resort. Two water taps together can fill the tank in $1\frac{7}{8}$ hours. The tap with longer diameter takes $2$ hours less than the tap with smaller one to fill the tank separately. Find the time in which each tap can fill the tank separately.

Amal and his family went for a trip to a resort. There are various amenities in the resort. There is a grass field in one corner of the resort. The area of the rectangular grass field is $560 \mathrm{sq}.\mathrm{m}.$ The area of another rectangular field is same as previous one but its length is $5 \mathrm{m}$  more and breadth is $2 \mathrm{m}$  less than the previous one. Find the length and breadth of the field.

Amal and his family went for a trip to a resort. There are various amenities in the resort. Amal's brother goes to a place of distance $8 \mathrm{km}$ from the resort and returns to the same resort by boat in $4$hours $16$ minutes. If the speed of the stream is $1 \mathrm{km}/\mathrm{hr}$. Find the speed of the boat he travelled in still water.

If the value of the discriminant of a quadratic equation is zero then the nature of the roots are