Recognising quadratic equations, forming them from word problems, solving by factorisation and using the discriminant to decide the nature of the roots. Our own step-by-step solutions to Exercises 4.1 to 4.3, one page per exercise, set out for step marks.
Each exercise has its own page with every question solved step by step. Pick the one you are on.
What it tests. An equation is quadratic when, after expanding and simplifying, it can be written as \(ax^2 + bx + c = 0\) with \(a \ne 0\). Always simplify first: an \(x^2\) term on both sides can cancel, and a cubic can reduce to a quadratic.
What it tests. Split the middle term: find two numbers whose product is \(ac\) and whose sum is \(b\), factorise, and set each factor to zero. In word problems, reject roots that make no sense (negative lengths, ages or counts) and say why.
What it tests. For \(ax^2 + bx + c = 0\), the discriminant is \(D = b^2 - 4ac\). \(D > 0\): two distinct real roots; \(D = 0\): two equal real roots \(x = -\dfrac{b}{2a}\); \(D < 0\): no real roots. The roots are \(x = \dfrac{-b \pm \sqrt{D}}{2a}\).
Quadratic Equations has 39 original board-style questions (MCQ, assertion–reason, short and long answers, case studies) with step mark schemes, revision notes and a four-step Route to 95. Three sample questions are open to everyone; a free account opens the rest.
Also useful: free MCQs and case studies for Quadratic Equations · Class 10 formula sheet · official CBSE board and sample papers · our sample papers with marking scheme · the Route to 95 plan
Textbook: NCERT Mathematics Class 10 (rationalised edition, 2023-24 reprint onward), free from ncert.nic.in. Question statements are shortened to the minimum needed; the solutions and tips are our own. CBSE Math Revision is independent and not affiliated with NCERT or CBSE. Spotted a slip? Tell us and it goes in the corrections log.