Solved Examples on Quadratic Equation
Let’s solve some questions on quadratic equations using its formula.
Example 1: Check whether the following equation is a quadratic equation or not. (x – 2)(x + 1) = (x – 1)(x + 3)
Solution:
We know that a quadratic equation must be of degree 2.
Let’s simplify and check the given equation.
(x – 2)(x + 1) = (x – 1)(x + 3)
⇒ x2 + x – 2x – 2 = x2 + 3x – x – 3
⇒ x2 – x – 2 = x2 + 2x – 3
⇒ -x – 2 = 2x – 3
⇒ -3x + 1 = 0
This equation is of degree 1. Thus, it cannot be a quadratic equation.
Example 2: Find the quadratic equation having the roots 4 and 9 respectively.
Solution:
The quadratic equation having the roots α, β, is (x – α)(x – β) = 0
Given,
α = 4, and β = 9
Therefore the required quadratic equation is,
(x – 4)(x – 9) = 0
x2 – 9x – 4x + 36 = 0
x2 – 13x + 36 = 0
Thus, the required quadratic equation is x2 – 13x + 36 = 0
Example 3: Quadratic equation 3x2 + 5x + 9 = 0 has roots α, and β. Find the quadratic equation having the roots 1/α, and 1/β.
Solution:
Given equation 3x2 + 5x + 9 = 0
Comparing with ax2 + bx + c = 0
a = 3, b = 5 and c = 9
α + β = -b/a = -5/3
αβ = c/a = 9/3 = 3
Roots of the new equation are 1/α and 1/β.
Sum of Roots = 1/α + 1/β = (α + β)/α β = (-5/3)×(1/3) = -5/9
Product of Roots = 1/α β = 1/3
Thus, the required quadratic equation is,
x2 – (Sum)x + Product = 0
x2 – (-5/9)x + 1/3 = 0
Simplifying,
9x2 + 5x + 3 = 0
Quadratic Equations: Formula, Method and Examples
A Quadratic equation is a second-degree equation that can be represented as ax2 + bx + c = 0. In this equation, x is an unknown variable, a, b, and c are constants, and a is not equal to 0. To solve it, you can use methods such as factoring, completing the square, or the quadratic formula. Each method helps find the values of x that satisfy the equation.
Quadratic Equation
Let’s learn how to solve Quadratic Equations using different methods in detail.
Table of Content
- What is Quadratic Equation?
- Quadratic Equation Standard Form
- Quadratic Equation Examples
- Roots of Quadratic Equation
- Quadratic Equations Formula
- Nature of Roots
- Discriminant
- Sum of Roots in Quadratic Equation
- Product of Roots in Quadratic Equation
- Writing Quadratic Equations using Roots
- How to Solve Quadratic Equation?
- Factorization Method
- Completing Square Method
- Graph Method
- Quadratic Equations Having Common Roots
- Maximum and Minimum Value of Quadratic Equation
- Quadratic Equation Sign Convention
- Solved Examples on Quadratic Equation
- Practice Questions on Quadratic Equation
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