Kindly check out the video below to learn about the Quadratic equations. Watch the video till the end to complete this task.
Quadratic Equations:
The chapter 'Quadratic Equations' carrying the weightage of \(6\) marks in the board examination. It covers concepts like Framing Quadratic Equation using given situation/case study, Solving Quadratic Equation by Factorisation, Solving Quadratic Equation by Quadratic Formula and Nature of Roots.
The most possible variation of question types that we can expect in the board exam, as per the previous year's question paper, are discussed below.
| Total Marks \(5\) to \(6\) | |
| Variation \(1\) | Variation \(2\) |
Total Mark \(= 6\)
|
Total Mark \(= 5\)
|
To prepare well for the board examination, it is necessary to understand the following concepts clearly.
- Quadratic Equation - Check whether the given equation is quadratic or not, Framing a quadratic equation for the given situation
- Solving Quadratic Equation - Factorisation Method, Quadratic Formula Method
- Nature of roots - Discriminants.
| Important Concept (Learning Outcomes) | Expected Question Type | Concept dealt with |
|
Quadratic Equations
|
Sec D
|
|
|
Solving Quadratic Equation
|
Sec A, Sec D, Sec E | |
|
Nature of roots
|
Sec A, Sec D |
Let us recall the concepts in Polynomial:
1. A quadratic equation in the variable \(x\) is of the form \(ax^2 + bx + c = 0\), where \(a\), \(b\), \(c\) are real numbers and \(a\neq 0\). A real number \(p\) is said to be a root of the quadratic equation \(ax^2+ bx + c = 0\), if \(ap^2+ bp+c = 0\). The zeroes of the quadratic polynomial \(ax^2+ bx + c\) and the roots of the quadratic equation \(ax^2+ bx + c = 0\) are the same.
2. Solving the quadratic equation can be done in two different ways:
- Solving by factorisation.
- Solving by the quadratic formula.
Solving by Factorisation: If we can factorise \(ax^2+ bx + c\), \(a\neq 0\), into a product of two linear factors, then the roots of the quadratic equation \(ax^2+ bx + c = 0\) can be found by equating each factor to zero.
Solving by the Quadratic Formula: The formula for finding the roots of the quadratic roots
\(ax^2+bx+c=0\) is \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
3. Nature of Roots: A quadratic equation \(ax^2+ bx + c = 0\) has
| Discrimnent | Type of Roots |
| \(b^2-4ac > 0\) | Real and Distinct |
|
\(b^2-4ac = 0\)
|
Real and Equal |
| \(b^2-4ac < 0\) | No Real Roots |