Thus, this equation has roots x = 2 and Completing the Squares MethodĪny equation ax 2 + bx + c = 0 can be converted in the form (x + m) 2 – n 2 = 0. Question 2: Find the roots of the following quadratic equation using the same method. Now this equation will be zero when either of these two terms of both of these terms are zero Question 1: Find out the solutions of the given quadratic equation using the factorization method. Take common factors from these and on equating the two expressions with zero after taking common factors and rearranging the equation we get the roots.Factor the first two as a group and the last two terms as another group.Then write x coefficient as the sum of these two numbers and split them such that you get two terms for x.Find two numbers such that the product of the numbers is ‘ac’ and the sum is ‘b’.Like ax 2 + bx + c = 0 can be written as (x – x 1)(x – x 2) = 0 where x 1 and x 2 are roots of quadratic equation. Factorization MethodĪ quadratic equation can be considered a factor of two terms. Let’s look at all three of these methods one by one through examples. There are three types of methods to find the solution of a quadratic equation: The points which satisfy this equation are called solutions or zeros of this quadratic equation. Let’s assume a quadratic equation P(x) = 0. Let’s simplify and check the given equation. We know that a quadratic equation must be of degree 2. Question 2: Check whether the following equation is a quadratic equation or not. Now after losing the candies, we are given that product of the number of candies they have is 124. Then Ravi must have “45 – x” candies because both of them had 45 candies. Formulate a quadratic equation for this problem. We are asked to find out the number of candies each one had in the beginning. The product of the number of candies both of them have now is 124.

Question 1: Rahul and Ravi together have 45 candies. In general, any second-degree polynomial P(x), when put like P(x) = 0 represents a quadratic equation. Where, a, b, c are real numbers and constants and a ≠ 0.Įxample: 4x 2 – 5x = 0, 5x 2 + 16x + 5 = 0 Quadratic EquationĪ quadratic equation in variable “x” is an equation of the form, Let’s define the quadratic equation formally. Then the length of the ground will be “2x + 50”. Let’s say the breadth of the ground is “x”. We need to find what should the length and breadth of the ground be. Coach instructs that the length of the ground must be 50 meters more than twice the breadth of ground. They’ve decided that the area of the football ground will be 1000m 2. Chemical Indicators - Definition, Types, Examplesįor example, a school board decides to make a football ground for their students.Class 10 RD Sharma Solutions- Chapter 2 Polynomials - Exercise 2.1 | Set 2.Euclid's Division Algorithm - Real Numbers | Class 10 Maths.Electric Potential and Potential Difference.

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Quadratic equations