Q3 of 16 Page 150

Find polynomials p(x) satisfying each set of conditions below.

First degree polynomial with p(1) = 1 and p(2) = 3.

let the polynomial be p(x)


p(x) = ax + b (where a and b are constants)


p(1) = a + b = 1 – (1) (given in the question)


p(2) = 2a + b = 3 – (2) (given in the question)


by (1) and (2)


a = 2, b = -1


⇒ p(x) = 2x – 1


More from this chapter

All 16 →
1

Write each of the relations below in algebra and see if it gives a polynomial. Give reasons for your conclusion also.

Two poles of heights 3 metres and 4 metres are erected upright on the ground, 5 metres apart. A rope is to be stretched from the top of one pole to some point on the ground and from there to the top of the other pole:



The relation between the distance of the point on the ground from the foot of a pole and the total length of the rope.

 2

Write each of the operations below as an algebraic expression, find out which are polynomials and explain why.

i) Sum of a number and its reciprocal.


ii) Sum of a number and its square root.


iii)Product of the sum of difference of a number and its square root.

 3

Find polynomials p(x) satisfying each set of conditions below.

First degree polynomial with p(1) = –1 and p(–2) = 3.

 3

Find polynomials p(x) satisfying each set of conditions below.

Second degree polynomial with p(0) = 0, p(1) = 2 and p(2) = 6.