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
Determine if 3 is a Root of the Equation Question: Determine if \(3\) is a root of the equation: \[ \sqrt{x^2-4x+3}+\sqrt{x^2-9} = \sqrt{4x^2-14x+16} \] Solution To check whether \(3\) is a root, substitute \(x=3\) into the equation. Left-Hand Side (LHS) \[ \sqrt{3^2-4(3)+3}+\sqrt{3^2-9} \] \[ =\sqrt{9-12+3}+\sqrt{9-9} \] \[ =\sqrt{0}+\sqrt{0} \] \[ =0+0 \] \[ =0 \]
Find the Value of k for which the Given Value is a Solution Question: Find the value of \(k\) for which the given value is a solution of the equation: \[ x^2+3ax+k=0 \] Given, \[ x=-a \] Solution Since \(x=-a\) is a solution, it must satisfy the given equation. Substituting \(x=-a\) into the equation: \[