Exercise 4.3 focuses on solving quadratic equations using the Quadratic Formula and understanding the nature of their roots (real, equal, or imaginary). It also covers word problems leading to quadratic equations.
Use the Quadratic Formula (Exercise 4.3’s primary method).
Yes: Factorization (if easily factorable, Ex. 4.2). Completing the Square (useful for deriving the formula). But Ex. 4.3 emphasizes the Quadratic Formula.
Step 1: Understand the problem and define variables. Step 2: Formulate the quadratic equation from given conditions. Step 3: Solve using the quadratic formula or factorization. Step 4: Reject invalid solutions (e.g., negative time/distance if not applicable).
NCERT Solutions Class 10 Maths Chapter 4 Quadratic Equations Exercise 4.3 helps students extend their problem-solving expertise in quadratic equations with two new methods. The exercise goes beyond the traditional factorisation method for solving the quadratic equations with the method of completing the square & the quadratic formula. These methods are mostly used when the quadratic equations don’t have a common term to form two binomials.
Here, you can find NCERT Solutions Class 10 Maths Chapter 4 Exercise 4.3 PDF, along with some important key concepts of the exercise in brief.
1.0Download NCERT Solutions Class 10 Maths Chapter 4 Quadratic Equations Exercise 4.3: Free PDF
2.0Introduction to Solutions of Quadratic Equations:
Let us first recall what solutions of a quadratic equation are before proceeding to the steps of solving quadratic equations. The solutions of any given quadratic equation are the variable values (mainly x), which set the equation to zero. They are determined when the quadratic equations have been expressed in their standard form. That is:
ax2+bx+c=0
In this expression, a and b are coefficients of the variable x, and c is the constant term. Solutions of quadratic equations are also referred to as the roots or the zeroes of the equations.
3.0Key Concepts of Exercise 4.3
Exercise 4.3 will look forward to the new methods of solving quadratic equations, understanding which will equip students with extra tools to find the zeroes of equations. Let’s explore important key concepts of these methods:
Completing the Square:
Completing the square method requires a proper approach to solving the quadratic equation, which includes the following:
Divide the Equation by a: The first and most important step of this method is dividing the given quadratic equation by the coefficient of x2, that is, “a”. This is performed to set the coefficient of x2 equal to 1 so that these equations are easier to solve.
Form a Perfect square: The next step of the method is to make the equation a perfect square trinomial. This is done by adding and subtracting the square of half of the coefficient of x.
Simplify the Equation: After finishing the square, rewrite the equation to create the product of binomials. Equalise these polynomials to zero to solve for the value of x. This equalisation gives rise to another method of solving quadratic equations, the direct formula or the quadratic formula for the equations.
The Quadratic Formula:
The expression derived from the method of completing the square forms a generalised formula for the quadratic equation ax2+bx+c=0. Which can be expressed as:
x=2a−b±b2−4ac
In the formula, b2 – 4ac can never be negative if the roots of a quadratic equation are real values. This generalised formula is also known as the quadratic formula for any equation. The formula is a useful tool in solving complex quadratic equations, which require long-form solutions of the equations.
4.0Exercise 4.3: Overview
The first couple of questions of exercise 4.3 includes solving the quadratic equations by completing the square method.
The Exercise also involves the solution of numerical problems of solving quadratic equations for roots by the quadratic formula.
Last but not least, the exercise also has some real-life problems to be solved with the aforementioned methods.
