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