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Quadratic Equation

Site: Newgate University Minna - Elearning Platform
Course: Basic Mathematics
Book: Quadratic Equation
Printed by: Guest user
Date: Monday, 6 April 2026, 2:47 PM

Description

The polynomial equation whose highest degree is two is called a quadratic equation.

There are different methods of solving quadratic equation in which you have learned in secondary school. Some of these methods will be reviewed again in this unit. The method of completing the square shall be studied and will be used to derive the general formula of quadratic equation which is popularly known as almighty formula. Quadratic equations shall be constructed using sum and product of the roots.

Table of contents

1. quadratic equations

A quadratic expression in one independent variable xx is generally written as:

ax2+bx+cax^2 + bx + c

where a,b,ca, b, c are constants, and a≠0a \neq 0 (otherwise, the equation becomes linear). A quadratic equation is written as:

ax2+bx+c=0ax^2 + bx + c = 0

Would you like me to generate some self-assessment exercises on quadratic expressions and equations? Here are a few you can try:

Self-Assessment Exercises:

  1. Solve the following quadratic equations using the quadratic formula:

    • x2−5x+6=0x^2 - 5x + 6 = 0

    • 2x2+3x−2=02x^2 + 3x - 2 = 0

  2. Factorize the following quadratic expressions:

    • x2−7x+12x^2 - 7x + 12

    • 3x2−2x−83x^2 - 2x - 8

  3. Find the roots of the quadratic equation by completing the square:

    • x2+4x−5=0x^2 + 4x - 5 = 0

  4. For the quadratic function f(x)=2x2−3x+4f(x) = 2x^2 - 3x + 4, determine:

    • The vertex

    • The axis of symmetry

    • Whether the parabola opens upwards or downwards