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Quadratic Equations

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Quadratic Equations - Lesson Summary

Quadratic equation:
An equation of the form ax 2 +bx +c = 0 is called a quadratic equation in one variable, where a, b, c are real numbers and a ≠ 0. It’s a second degree polynomial.

Zeroes or Roots of a Quadratic Equation
Let ax 2 +bx +c = 0 be the quadratic equation , If aα 2 + bα + c = 0 then α is called the zero or root of the quadratic equation.

There are various methods to solve the quadratic equation, they are (i) Factorization (ii) Completing the squares (iii) Quadratic Formula (iv) Graphical Representation.

Factorization method
In factorization method the quadratic equation is solved by splitting them into factors.

Completing the squares
In completing squares the quadratic equation is converted into either (a + b) 2 or ( a - b) 2.

Quadratic Formula
The quadratic formula to find the roots of quadratic equation are  - b ± b 2 - 4 a c 2 a ,  where b 2 - 4ac is called the discriminant of the quadratic equation and it is denoted by D or Δ.

The sum of the roots of the quadratic equation is  - b a  or - Coefficient of  x       Coefficient of   x 2   and the product of the roots of the quadratic equation is  c a  or   Constant term       Coefficient of   x 2   .

Nature of the roots

If D = 0 roots are real and equal , D > 0 roots are real and unequal, D < 0 roots are imaginary.

The graph of a quadratic equation is a parabola. It depends on the value of ‘a’, if a > 0 the parabola opens upwards, a < 0 parabola opens downwards.

If D > 0 parabola intersects x-axis at two distinct points, D < 0 parabola does not intersect the parabola and D = 0 parabola touches x-axis at only one point.


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