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CBSE Guess > eBooks > Class X > Maths by Mr. M. P. Keshari

Chapter 4: Quadratic Equations

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1. Quadratic Polynomials:

The general form of a quadratic polynomial in x is ax2 + bx + c

where a,b,c, are real numbers and

2. Zeros of quadratic polynomials

When a quadratic polynomial is equated to zero, we get two values of x which is called zeros of a quadratic polynomial.

3. Quadratic Equations

A quadratic polynomial equated to zero is called a quadratic equation. The general form of a quadratic equation is ax2 + bx + = 0, where a, b, c are real numbers and

4. Quadratic formula

Let ax2 + bx + c = 0

Multiplying by 4a we get

4a2x2 + 4abx + 4ac = 0

Or, (2ax)2 + 2.2ax.b + b2 = b2 - 4ac

Or, (2ax + b)2

= b2 - 4ac

Let D = b2 - 4ac


If is not real and, there fore, the equation has no real roots.

"D" is called the discriminat of the quadratic equation.

Case-I, When

i. e. then the equation has two distinct real roots given by

Case-II, when D = b2 - 4ac = 0

Both the roots are real and equal.


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