Educational

Quadratic Equation – Exercise 4.3 Solutions (Step-by-Step Guide)    Solve the following quadratic equations by factorization: (x − 4)(x + 2) = 0 Watch Solution (2x + 3)(3x − 7) = 0 Watch Solution 3x² − 14x − 5 = 0 Watch Solution 9x² − 3x − 2 = 0 Watch Solution 1/(x − 1) − […]

Solve the Quadratic Equation by Factorization: (x – 4)(x + 2) = 0 Question: Solve the following quadratic equation by factorization: $$ (x-4)(x+2)=0 $$ Solution $$ (x-4)(x+2)=0 $$ Either $$ x-4=0 $$ $$ x=4 $$ or $$ x+2=0 $$ $$ x=-2 $$ Hence, $$ \boxed{x=4,\,-2} $$ Next Question / Full Exercise

A Train Travels 360 km at a Uniform Speed Question: A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hour less for the same journey. Form the quadratic equation to find the speed of the train. Solution Let the speed of the

Express Train and Passenger Train Problem – Form the Quadratic Equation Question: An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore. If the average speed of the express train is 11 km/hr more than that of the passenger train, form the quadratic equation to find

Height of a Right Triangle is 7 cm Less Than Its Base Question: The height of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, form the quadratic equation to find the base of the triangle. Solution Let the base of the triangle be \[ x \text{ cm}

A Cottage Industry Produces Toys – Form the Quadratic Equation Question: A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of articles produced in a day. On a particular day, the total cost of production

John and Jivanti Together Have 45 Marbles Question: John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Form the quadratic equation to find how many marbles they had to start with, if John had \(x\) marbles. Solution

The Product of Two Consecutive Positive Integers is 306 Question: The product of two consecutive positive integers is 306. Form the quadratic equation to find the integers, if \(x\) denotes the smaller integer. Solution Let the smaller positive integer be \[ x \] Then the next consecutive positive integer is \[ x+1 \] According to

Find the Values of a and b from Given Roots Question: If \[ x=\frac{2}{3} \quad \text{and} \quad x=-3 \] are the roots of the equation \[ ax^2+7x+b=0, \] find the values of \(a\) and \(b\). Solution Given roots: \[ \alpha=\frac{2}{3}, \qquad \beta=-3 \] For the quadratic equation \[ ax^2+7x+b=0, \] \[ \alpha+\beta=-\frac{7}{a} \] and \[

RD Sharma Chapter 4 : Quadratic Equation – Exercise 4.2 Solutions The product of two consecutive positive integers is 306. form the quadratic equation to find the integers, if x denotes the smaller integer.  Watch Solution John and Jivanti together have 45 marbles. both of them lost 5 marbles each, and the product of the number