CBSE Class 10 Maths Formulas for Chapter 4 Quadratic Equations are mentioned in this article. You can also check here all major definitions, properties and identities. Having all the key terminologies at one place will help you quickly revise the chapter and save your time for the practice of questions on quadratic equations.
Check all formulas below:
1. ax^{2}+bx+c = 0, a≠0 is the standard form of a quadratic equation, where a, b and c are real numbers.
2. Solution of a Quadratic Equation
A real number α is called a root of the quadratic equation ax^{2} + bx + c = 0, a ≠ 0 if a α^{2} + bα + c = 0.
Here, x = α is a solution of the quadratic equation.
3. Quadratic equation can be solved by:
Factorisation method: Given quadratic equation ax^{2} + bx + c = 0 is factorised by splitting its middle term and written as a product of two linear factors, then the roots of the quadratic equation can be found by equating each factor to zero.
Completing square: A quadratic equation can also be solved by the method of completing the square.
(i) a^{2} + 2ab + b^{2} = (a +b)^{2}
(ii) a^{2} − 2ab + b^{2} = (a − b)^{2}
Also Check: MCQs for Class 10 Maths All Chapters
4. Quadratic Formula: If b^{2} – 4ac ≥ 0, then the roots of the quadratic equation ax^{2} + bx + c = 0 are given by
This formula is known as Quadratic Formula.
5. Discriminant: Discriminant of a quadratic equation ax^{2} + bx + c = 0, a ≠ 0 is given by
D = b^{2 }− 4ac
6. Nature of roots:
A quadratic equation ax^{2 }+ bx + c = 0, a≠0 has :
i. Two distinct and real roots, if b^{2}−4ac > 0
ii. Two equal and real roots, if b^{2}−4ac = 0
iii. No real roots, if b^{2}−4ac < 0.
7. If roots of a quadratic equation are given, then the quadratic equation can be represented as:
x^{2} – (sum of the roots)x + product of the roots = 0
8. Sum of roots = –b/a
9. Product of roots = c/a
10. Boats and Streams
(i) Downstream: The direction along the stream of water is called downstream.
(ii) Upstream: The direction against the stream of water is called upstream.
(iii) Let the speed of a boat in still water be u km/hr and the speed of the stream be v km/hr, then
Speed downstream = (u + v) km/hr
Speed upstream = (u − v) km/hr.
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