Bihar Board Class 10 · Maths · Matric exam 2027
Chapter 4: Quadratic Equations — notes
The chapter’s 6 parts in the book’s order — the first idea of each and the points Medha Ma’am writes on the board — and the summary at the end. The full lesson and a check question for each part are in the app.
1. What is a Quadratic Equation
Okay, so you already know about polynomials.
- • Quadratic equation: ax2 + bx + c = 0, a ≠ 0
- • Example: 2x² + x − 300 = 0
- • breadth = x m, length = (2x+1) m
- • area = (2x+1).x = 2x² + x = 300
2. Checking if an Equation is Quadratic
Sometimes an equation looks complicated, but once you simplify it, you must check whether, after bringing everything to one side, it takes the form ax² + bx + c = 0 with a not zero.
- • (x−2)2+1 = 2x−3 → x2−6x+8 = 0 (quadratic)
- • x(x+1)+8 = (x+2)(x−2) → x+12 = 0 (not quadratic)
- • (x+2)3 = x3−4 → x2+2x+2 = 0 (quadratic)
3. Solving by Factorisation
Okay, so let's talk about roots of a quadratic equation.
- • 2x²−5x+3 = 0
- • =2x²−2x−3x+3 = 0
- • =2x(x−1) − 3(x−1) = 0
- • =(2x−3)(x−1) = 0
- • roots: x = 3/2, x = 1
4. Solving by Completing the Square
Okay, so there's another method called completing the square.
- • x2+4x−5 = 0 → (x+2)2-9 = 0
- • (x+2)2 = 9 → x+2=±3
- • x = 1 or x=-5
- • 3x²−5x+2 = 0 → roots x = 1, x = 2/3
5. The Quadratic Formula
Okay, so let's get a formula that works for every quadratic equation.
- • Quadratic formula: x = [-b ± √(b2−4ac)] / 2a
- • Example: 2x²+x−528 = 0, a = 2,b = 1,c=-528
- • x = [-1 ± √(1+4224)]/4 = [-1±65]/4
- • x = 16 or x=-33/2 → breadth = 16m, length = 33m
6. Nature of Roots
Okay, so look at the board.
- • Discriminant = b2−4ac
- • b2−4ac>0: two distinct real roots
- • b2−4ac = 0: two equal real roots
- • b2−4ac<0: no real roots
- • Example: 2x²−4x+3 = 0 → disc=-8 → no real roots
Summary
Okay, so let's look back at everything we did in this chapter. We started with a real-life situation — remember the prayer hall problem? — and saw how it leads to an equation of the form ax² + bx + c = 0, with a not zero. That's a quadratic equation. You also learnt to check an equation carefully — sometimes after simplifying, it may or may not stay quadratic. Then we found roots in three ways. First, factorisation, by splitting the middle term. Second, completing the square, where we write the equation as (x + a)² − b² = 0. And third, the general formula — x = [−b ± √(b² − 4ac)] / 2a. This one works for any quadratic equation. Last, we looked at the discriminant, b² − 4ac. It tells us the nature of the roots — two distinct real roots, two equal real roots, or no real roots — and we can know this without even solving the equation fully. Tell me — of these three methods, which one did you find the easiest to work with?
AskMedha · Medha Ma’am — Bihar Board Class 10 Maths, Chapter 4. Written from the textbook, checked twice.
Questions parents and students ask
- How do I get the "Quadratic Equations" notes as a PDF?
- Press "Save as PDF" — the phone’s print sheet opens; choose "Save as PDF" there. The PDF holds the notes only.
- Where are these notes written from?
- From the chapter’s own textbook text, part by part, in the book’s own terms; a second, independent model then checked every part against the book. The full lesson, a check question for each part and the practice are in the AskMedha app.
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