Class 10 Maths - CBSE
Quadratic Equations
The chapter Quadratic Equations in Class 10 CBSE Mathematics builds upon polynomial concepts to introduce equations of degree two, having the standard form ax^2 + bx + c = 0. Students learn to find the roots or solutions of these equations using three primary methods: factorisation, completing the square, and the quadratic formula. A crucial part of this chapter is the discriminant (b^2 - 4ac), which determines the nature of roots. This chapter carries significant weight in the CBSE board exams, frequently appearing in 3-mark and 4-mark questions, including practical word problems that test real-life problem-solving skills.
Start Learning FreeKey Concepts
Standard Form of Quadratic Equation
Any equation of the form ax^2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0, is called a quadratic equation.
Roots of a Quadratic Equation
The values of the variable x that satisfy the quadratic equation are called its roots or solutions, which are geometrically the x-intercepts of its graph.
Solution by Factorisation
Splitting the middle term of the quadratic expression into two parts so that the equation can be factored into two linear factors.
The Quadratic Formula
A direct formula, x = (-b ± √(b^2 - 4ac)) / 2a, used to find the roots of any quadratic equation without needing to factorise.
Discriminant and Nature of Roots
The expression D = b^2 - 4ac determines whether the roots are real and distinct (D > 0), real and equal (D = 0), or non-real (D < 0).
Important Formulas
Board Exam Info
In the CBSE Class 10 Mathematics board exam, Quadratic Equations typically carry around 5 to 8 marks. Questions usually include 1-mark multiple-choice questions, 2-mark computational questions using the quadratic formula or factorisation, and 3 to 4-mark word problems based on age, speed-distance-time, or geometry.
Frequently Asked Questions
How do I know whether to use factorisation or the quadratic formula?
Try factorisation first because it is faster. If the middle-term splitting is difficult or gives messy fractions, immediately switch to the quadratic formula.
What does a negative discriminant mean for my answer?
If D = b^2 - 4ac is negative, it means the equation has no real roots, and you can write 'no real roots exist' and stop solving for Class 10 level.
How do I frame equations correctly for word problems?
Identify the unknown quantity to be found and let it be x. Read the statement sentence by sentence to translate conditions into mathematical expressions step by step.
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