class 10 , chapter 3 , cbse , polynomials project , maths

1. POLYNOMIALS
MATHS PROJECTS
AVI

2. TYPES OF POLYNOMIALS
Types of polynomials are –
1] Constant polynomial
2] Linear polynomial
3] Quadratic polynomial
4] Cubic polynomial
5] Bi-quadratic polynomial

3. ZERO OF A POLYNOMIAL
• A real number k is said to a zero of a
polynomial p(x), if said to be a zero of a
polynomial p(x),if p(k)= 0
• For example, consider the polynomial
p(x) = x³3x4. Then,
p(1) = (1)²  (3(1)  4 = 0
• Also, p(4) = (4)²  (3 4)  4 = 0
• Here,  1 and 4 are called the zeroes of
the quadratic polynomial x²  3x  4 .

4. GEOMETRICAL MEANING OF
THE ZEROES OF A POLYNOMIAL
*We know that a real number k is a zero
of the polynomial p(x) if p(K) = 0 . But to
understand the importance of finding
the zeroes of a polynomial, first we shall
see the geometrical meaning of –
*1) Linear polynomial .
*2) Quadratic polynomial
*3) Cubic polynomial

5. GEOMETRICAL MEANING OF
LINEAR POLYNOMIAL
*For a linear polynomial
ax  b , a  0, the graph of
y = ax b is a straight line
. Which intersect the x
axis and which intersect
the x axis exactly one
point ( b  2 , 0 ) .
Therefore the linear
polynomial ax  b , a  0
has exactly one zero .

6. QUADRATIC POLYNOMIAL
*For any quadratic
polynomial ax²bxc,a0,
graph of the
corresponding equation y
=ax²bxc has one of the
two shapes either open
upwards or open
downward depending on
whether a0 or a0.These
curves are called
parabolas .

7. CUBIC POLYNOMIAL
*The zeroes of a cubic
polynomial p(x) are thex
coordinates of the point
where the graph of y =
p(x) intersect the x–axis .
Also,there are at most 3
zeroes for the cubic
polynomials.In fact, any
polynomial of degree 3
can have at most three
zeroes

8. How do People use Polynomials?
*Engineers use polynomials to graph the
curves of roller coasters Since polynomials
are used to describe curves of various
types, people use them in the real world
to graph curves. For example, roller
coaster designers may use polynomials to
describe the curves in their rides.
Combinations of polynomial functions are
sometimes used in economics to do cost
analyses, for example.

9. Polynomials for Modeling or
Physics
Polynomials can also be used to model
different situations, like in the stock market
to see how prices will vary over time. Business
people also use polynomials to model markets,
as in to see how raising the price of a good
will affect its sales.. Polynomial integrals (the
sums of many polynomials) can be used to
express energy, inertia and voltage
difference, to name a few applications.

10. Polynomials in Industry
*For people who work in industries that deal
with physical phenomena or modeling
situations for the future, polynomials come
in handy every day. These include everyone
from engineers to businessmen. For the rest
of us, they are less apparent but we still
probably use them to predict how changing
one factor in our lives may affect
anotherwithout even realizing it.

11. THANK YOU
*SAPPHIRE HOUSE MEMBERS
– KHURRAM, ROJO,
NASIR,AYAN,AFNAN,TIMOTHY