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Quadratic Equations




What is Quadratic Polynomial

P(x) = ax2 +bx+c   where a≠0

It is a polynomial of degree 2
Examples:

$P(x) =3x^2-11x-2$
$P(x)=x^2 -x -11$
$P(x)=x^2 + x -897$

Graphing quadratics Polynomial


Lets us assume y= p(x) where p(x) is the polynomial of quadratic type Now we can plot the equation y=p(x) on the Cartesian plane by taking various values of x and y obtained by putting the values. The plot or graph obtained can be of any shapes The zero's of the polynomial are the points where the graph meet x axis in the Cartesian plane. If the graph does not meet x axis ,then the polynomial does not have any zero's. Let us take some useful polynomial and shapes obtained on the Cartesian plane Open Upward and downward Parabola
Open Upward parabola intersecting at single point and Open upward Parabola having no zeroes
Open Downward Parabola having no zeroes

what is a quadratic equation

When we equate Quadratic Polynomial with zero, it is called Quadratic equation
$ax^2 +bx+c =0$ where a ≠0
Examples:

$6x^2-x-2=0$
$x^2 -x -20=0$
$x^2 + x -300 = 0$

It is used in many field and it has many application in Mathematics
For example
John has a area of a rectangular plot is 528 m2.The length of the plot (in meters) is one more than twice its breadth. We need to find the length and breadth of the plot
For solution , we can assume breadth is x ,then lenght would be (2x+1)
Now $528=x(2x+1)$
or $2x^2+x -528 =0$
Which is a quadratic equation and the required representation of the problem mathematically
Solution or root of the Quadratic equation
A real number $\alpha$ is called the root or solution of the quadratic equation if
$a \alpha^2 +b \alpha +c=0$

Some other points to remember
  • The root of the quadratic equation is the zeroes of the polynomial p(x).
  • We know from chapter two that a polynomial of degree can have max two zeroes. So a quadratic equation can have maximum two roots
  • A quadratic  equation has no real roots if b2- 4ac < 0
  • A graphing quadratic  equation is same as graphing quadratic polynomial as explained above

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Reference Books for class 10

Given below are the links of some of the reference books for class 10 math.

  1. Oswaal CBSE Question Bank Class 10 Hindi B, English Communication Science, Social Science & Maths (Set of 5 Books)
  2. Mathematics for Class 10 by R D Sharma
  3. Pearson IIT Foundation Maths Class 10
  4. Secondary School Mathematics for Class 10
  5. Xam Idea Complete Course Mathematics Class 10

You can use above books for extra knowledge and practicing different questions.


Class 10 Maths Class 10 Science

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