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

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.

A motorboat 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.

In a flight of $600 \mathrm{km}$, an aircraft was slowed due to bad weather. Its average speed for the trip was reduced by $200 \mathrm{km}/\mathrm{hr}$ and time of flight increased by $30$ minutes. Find the original duration of flight.

Solve the equation $x^2-12x+27=0$  by using formula.

Find the value of the determinant of the quadratic equation $2x^2-5x-1=0$, and hence write the nature of its roots.

Solve $2x^2-5x+3=0$ by using the formula.

Some students planned a picnic. The budget for food was $₹480$. But eight of these failed to go and thus the cost of food for each member increased by $₹10$. How many students attended the picnic $?$

The product of two consecutive positive integers is $30$. This can be expressed algebraically as