Quadratic Equation definition: A quadratic equation in x is an equation that can be written in the form of

a\;x^2-bx+c=0\;\;\;\;\;\;\;\;\;\;\;\;\;;a,\;b,\;c are real numbers and a ≠ 0.
Another name for a quadratic equation in x is 2nd Degree Polynomial in x.

Quadratic Equation Examples: The following equations are the quadratic equations:

  • x^2-7x+9=0\;\;\;\;\;\;\;\;\;\;\;\;\;;a=1,\;b=-7,\;c=9
  • 5x^2+8x-9=0\;\;\;\;\;\;\;\;\;\;\;\;\;;a=5,\;b=8,\;c=-9
  • -7 x^2-9x-8=0\;\;\;\;\;\;\;\;\;\;\;\;\;;a=-7,\;b=-9,\;c=-8

Solution of Quadratic Equations:

By Factorization: It involves factoring the polynomial

a\;x^2-bx+c=0\;\;\;\;\;\;\;\;\;\;\;\;\;;a,\;b,\;c are real numbers and a ≠ 0.

It makes use of the fact that if xy = 0, then x = 0 or y = 0.
For Example:

If (x - 2) (x - 4) = 0, then either x - 2 = 0 or x - 4 = 0

Example 1: Solve the equation x^2-7x+10=0 by factorization.
Solution:

quadratic equation

x^2-7x+10=0 .

x^2-5x-2x+10=0

x(x-5)-2(x-5)=0
(x - 2) (x - 5) = 0.

∴ either x - 2 = 0x = 2
or x - 5 = 0x = 5
∴ the given equation has two solutions: 2 and 5

so Solution set = {2,5}

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