Question

2. Let p(x) be a cubic polynomial such that coefficient
of x^3 is 1, p(1) = 1, p(2) = 2 and p(3) = 3, then the
value of p(4) is
(1) 4
(3) 10
(4) 7
(2) 6

pls send solved
i will mark brainliest​

Answer 1

Answer:

(3) - 10

Step-by-step explanation:

Let the cubic polynomial be p(x) = ax³ + bx² + cx + d.

Given that coefficient of x³ is 1.

(i)

When x = 1:

p(1) = 1 * a + b + c + d

⇒ 1 = 1 + b + c + d

⇒ b + c + d = 0

(ii)

When x = 2:

p(2) = 1(2)³ + b(2)² + c(2) + d

⇒ 2 = 8 + 4b + 2c + d

⇒ 4b + 2c + d = -6

(iii)

When x = 3:

p(3) = a(3)³ + b(3)² + c(3) + d

⇒ 3 = 27 + 9b + 3c + d

⇒ 9b + 3c + d = -24

On solving (i) & (iii), we get

b + c + d = 0

9b + 3c + d = -24

--------------------------

-8b - 2c = 24

8b + 2c = -24

4b + c = -12      ----------------------------- (iv)

On solving (ii) & (iii), we get

4b + 2c + d = -6

9b + 3c + d = -24

---------------------------

-5b - c = 18  

5b + c = -18            -------------------------- (v)

On solving (iv) & (v), we get

4b + c = -12

5b + c = -18

--------------------

-b = 6

b = -6

Substitute b = -6 in (iv), we get

4b + c = -12

⇒ 4(-6) + c= -12

⇒ -24 + c = -12

⇒ c = 12

Substitute in (i), we get

⇒ b + c + d = 0

⇒ 12 - 6 + d = 0

⇒ d = -6

Now,

p(4) = 4³ + (-6)(4)² + 12(4) - 6

      = 64 - 96 + 48 - 6

      = 10

Therefore, the value of p(4) is 10.

Hope it helps!

Answer 2

Hope it helps you !......