Question

Find polynomial p(x) satisfying each set of conditions below. i) First degree polynomial with p(1)=1 and p(2)=3 . ii) First degree polynomial with p(1)=-1 and p(-2)=3 .​

Answer 1

Answer:

required polynomials are 2x-1 and  -4/3 x^2 + 1/3

Step-by-step explanation:

(i) let the first degree polynomial be p(x) = a x + b

p(1) = a + b = 1 → (1)

p(2) = 2a + b = 3 → (2)

(2) - (1) ,

a = 2

∴ b = -1

required polynomial is 2x-1

(ii)  Let the required polynomial be p(x) = cx + d

p(1) = c + d = -1 →(3)

p(-2) = -2c + d = 3 →(4)

(4) - (3) ,

-3c = 4

⇒ c = -4/3

∴ d = 1/3

required polynomial is -4/3 x^2 + 1/3