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

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