In a polynomial p(x) = 2x3 + ax2 – 7x + b. p(1) = 3, p(2) = 19. Then

1.	In a polynomial p(x) = 2x3 + ax2 – 7x + b. p(1) = 3, p(2) = 19. Then find the value of ‘a’ and ‘b’?
Answer» p(x) = 2x³ + ax² – 7x + b We have p(1) = 3. p(1) = 2 x 1³ + a x 1² – 7 x 1 + b = 3 2 + a – 7 + b = 3 a + b – 5 = 3 a + b = 8 ………. (1) We have p(2) = 19. p(2 ) = 2 x 2³ + a x 2² – 7 x 2 + b = 19 16 + 4a – 14 + b = 19 4a + b + 2 = 19 4a + b = 17…….. (2) From equation (1), (2) (2) – (1) 4a + b = 17 \(\frac{a+b=8}{3a=9}\) a = 9/3 = 3 From equation (1) a + b = 8 3 + b = 8 b = 5

In a polynomial p(x) = 2x3 + ax2 – 7x + b. p(1) = 3, p(2) = 19. Then find the value of ‘a’ and ‘b’?

Answer»

p(x) = 2x³ + ax² – 7x + b

We have p(1) = 3.

p(1) = 2 x 1³ + a x 1² – 7 x 1 + b = 3

2 + a – 7 + b = 3

a + b – 5 = 3

a + b = 8 ………. (1)

We have p(2) = 19.

p(2 ) = 2 x 2³ + a x 2² – 7 x 2 + b = 19

16 + 4a – 14 + b = 19

4a + b + 2 = 19

4a + b = 17…….. (2)

From equation (1), (2)

(2) – (1) 4a + b = 17

\(\frac{a+b=8}{3a=9}\)

a = 9/3 = 3

From equation (1)

a + b = 8

3 + b = 8

b = 5