## Class 10 Chapter 2(Poloynomials)

**Case based 1: ****SLV-3 was successfully launched on july 18, 1980 from Shriharikota Range (SHAR), when Rohini satellite, RS-1, was placed in orbit, thereby making India the sixth member of an exclusive club of space-faring nations. SLV-3 employed an open loop guidance (with stored pitch programme) to steer the vehicle in flight along a pre-determined trajectory. The successful culmination of the SLV-3 project showed the way to advanced launch vehicle projects such as augmented Satellite Launch Vehicle (ASLV), Polar Satellite Launch Vehicle (PSLV) and Geosynchronous Satellite Launch Vehicle(GSLV).**

**A toy rocket is fired into the air from the top of a tall building Let its height above the ground after time t second be given by the P(t) = 24 t²-41 t + 12 **

**(A) What will be the shape of the graph representing the height of the rocket above the ground ?**

**(B) Find the zeros of the graph represented by P(t) = 24 t²-41 t + 12 **

### Solution:

* (A)* As the height of the rocket above the ground is given by a quadratic polynomial.

*P(t) = 24 t²-41 t + 12 .***Its graph will be a Parabola.**

**(B) To find the zeroes of the given polynomial by splitting the middle term.**

**P(t) = 24 t² – 41 t+12**

** = 24 t² -32 t – 9 t +12**

** = 8 t(3 t-4) – 3(3 t – 4)**

** = (3 t -4)(8 t – 3)**

**Therefore, zeroes are t = 3/8, 4/3.**

## Some other question

#### Question 1:Prove that 2-√3 is irrational, given that root 3 is irrational

#### Question 2:Prove that √5 is an irrational number

#### Question 3: Prove that √p + √q is irrational

#### Question 4:Prove that root 2 + root 5 is irrational