- Quadratic Polynomial
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- Graphing quadratics Polynomial
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- what is a quadratic equation
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- How to Solve Quadratic equations
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- Factoring quadratics equations
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- Solving quadratic equations by completing the square
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- Solving quadratic equations by using Quadratic formula
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- Nature of roots of Quadratic equation
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- Problem based on discriminant of a quadratic equation
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- Quadratic word problems

- NCERT Solutions Quadratic Equation Exercise 1
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- NCERT Solutions Quadratic Equation Exercise 2
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- NCERT Solutions Quadratic Equation Exercise 3
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- NCERT Solutions Quadratic Equation Exercise 4

P(x) = ax

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 -897097

P(x) =3x

P(x)=x

P(x)=x

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

When we equate Quadratic Polynomial with zero, it is called Quadratic equation

ax

Examples:

6x^{2}-x-2=0

x^{2} -x -20=0

x^{2} + x -300 = 0

6x

x

x

It is used in many field and it has many application in Mathematics

John has a area of a rectangular plot is 528 m

For solution , we can assume breadth is x ,then lenght would be (2x+1)

Now 528=x(2x+1)

or 2x

Which is a quadratic equation and the required representation of the problem mathematically

A real number α is called the root or solution of the quadratic equation if

aα

- 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 b
^{2}- 4ac < 0 - A graphing quadratic equation is same as graphing quadratic polynomial as explained above

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