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Chapter 4: Quadratic Equations
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.
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.
Maths by Mr. M. P. Keshari