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

Represent the following situations in the form of quadratic equation: "The area of a rectangular plot is $528 {\mathrm{m}}^2$. The length of the plot (in $\mathrm{metres}$) is one more than twice its breadth". We need to find the length and breadth of the plot.

Represent the following situation in the form of quadratic equation:

The product of two consecutive positive integers is $306$. We need to find the integers.

Represent the following situation in the form of quadratic equation:

Rohan's mother is $26 \mathrm{years}$ older than him. The product of their ages after $3 \mathrm{years}$ will be $360 \mathrm{years}$. We need to find Rohan's present age.

Represent the following situation in the form of quadratic equation:

A train travels a distance of $480 \mathrm{km}$ at a uniform speed. If the speed had been $8 \mathrm{km}/\mathrm{hr}$ less, then it would have taken $3 \mathrm{hours}$ more to cover the same distance. We need to find the speed of the train.

Find the roots of the following quadratic equations by quadratic method.

$2x^2+x-4=0$

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

$5x^2-7x-6=0$

$x^2+5=-6x$

In a class test, the sum of Moulika's marks in Mathematics and English is $30$. If she got $2$ marks more in Mathematics and $3$ marks less in English, the product of her marks would have been $210$. Find her marks in the two subjects.

Find two numbers whose sum is $27$ and product is $182$.

Find two consecutive positive integers, sum of whose squares is $613$.