Embibe Experts Solutions for Chapter: Quadratic Equations, Exercise 1: CBSE-2022 (Delhi - II)

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.

A train travels at a certain average speed for a distance of $63 \mathrm{km}$ and then travels at a distance of $72 \mathrm{km}$ at an average speed of $6 \mathrm{km}/\mathrm{hr}$ more than its original speed. If it takes $3$hours to complete total journey, what is the original average speed ($\left(\mathrm{km}/\mathrm{hr}\right)$?

For what values of $k$, the roots of the equation $x^2+4x+k=0$ are real?

Find the value of $k$ for which the roots of the equation $3x^2-10x+k=0$ are reciprocal of each other.

Find the value of $k$ such that the polynomial $x^2-\left(k+6\right)x+2\left(2k-1\right)$ has sum of its zeros equal to half of their product.

Two water taps together can fill a 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.

Find a quadratic polynomial whose zeros are reciprocals of the zeros of the polynomials $f\left(x\right)=a{x}^2+bx+c, a\ne 0, c\ne 0.$

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.