Question

.B) If the polynomials 3x3 + ax2 + 3x +5 and 4x3+x2–2x +a leaves the same remainder when divided by (x-2), then show that the value of a= -1.​​

Answer 1

Answer:

Step 1:- Let the given polynomials be p(x) and f(x)

Step 2:- According to the question

p(2) = f(2)

⇒ 3(2)³ + a(2)² + 3(2) + 5 = 4(2) ³ + (2)² - 2(2) + a

⇒ (3 × 8) + 4a + 6 + 5 = 4 × 8 + (4 - 4) + a

⇒  35 + 4a = 32 + a

⇒ 3a = -3

∴ a = -1

Step 3:- Hence, a = -1

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Step 1:- Let the given polynomials be p(x) and f(x)

Step 2:- According to the question p(2) = f(2)

3(2)³ + a(2)² + 3(2) + 5 = 4(2) ³ + (2)² - 3

2(2) + a

(3 x 8) + 4a + 6+5 = 4 x 8 + (4-4) + a

→ 35 + 4a = 32 + a

→ 3a = -3

a=-1

Step 3:- Hence, a = -1