Quadratic Equations

For the 2025–2026 academic year, the most important topics in Class 10 Maths for the chapter on

Quadratic Equations focus on the standard form, finding real roots using factorization and the quadratic formula, and determining the nature of roots using the discriminant. Questions related to real-life applications are also emphasized. 

Core topics in quadratic equations 

Standard form 

• You must be able to identify if a given equation is a quadratic equation by checking if it can be rearranged into the standard form: ax2+bx+c=0a x squared plus b x plus c equals 0𝑎𝑥2+𝑏𝑥+𝑐=0, where a≠0a is not equal to 0𝑎≠0.
• Practice simple problems where you have to form the quadratic equation from a given word problem. 

Finding solutions (roots) of quadratic equations 

• Factorization: Learn to find the roots of a quadratic equation by splitting the middle term and factorizing the polynomial.
• Quadratic Formula: Master the use of the quadratic formula to find the roots, especially for equations that are not easily factorable. The formula is:
  x=−b±b2−4ac2ax equals the fraction with numerator negative b plus or minus the square root of b squared minus 4 a c end-root and denominator 2 a end-fraction𝑥=−𝑏±𝑏2−4𝑎𝑐√2𝑎
  This formula is crucial for solving all quadratic equations with real roots. 

Nature of roots 

• Discriminant (Dcap D𝐷): The discriminant, D=b2−4accap D equals b squared minus 4 a c𝐷=𝑏2−4𝑎𝑐, is used to determine the nature of the roots without actually solving the equation.
• Three conditions: Based on the value of the discriminant, you should be able to state the nature of the roots:
  • D>0cap D is greater than 0𝐷>0: Two distinct real roots.
  • D=0cap D equals 0𝐷=0: Two equal (or coincident) real roots.
  • D<0cap D is less than 0𝐷<0: No real roots (the roots are imaginary). 

Situational problems 

• Expect word problems from various day-to-day activities that require forming and solving a quadratic equation to find the solution.
• Common themes for word problems include speed and distance, time and work, area of geometric shapes, and age-related problems.
• Practice problems that can be reduced to quadratic equations by using a substitution, such as those involving fractions with variable denominators. 

Removed topic for 2025–2026 

• Completing the Square: The method of completing the square is no longer included in the syllabus for finding the roots of a quadratic equation. However, the derivation of the quadratic formula relies on this method, so a conceptual understanding may still be helpful.