Question

answer with full explanation plz......​

Answer 1

Given Polynomial ⇒

P(x) = x⁴ - 2x³ + 3x² - ax + 3a - 7.

Divisor = x + 1

∴ x + 1 = 0

∴ x = -1

Thus,

P(-1) = (-1)⁴ - 2(-1)³ + 3(-1)² - a(-1) + 3a - 7.

19 = 1 + 2 + 3 + a + 3a - 7

19 = 6 - 7 + 4a

4a - 1 = 19

4a = 20

⇒ a = 5

∴ Value of a is 5.

Now, the Polynomial will be ⇒

P(x) = x⁴ - 2x³ + 3x² - (5)x + 3(5) - 7

P(x) = x⁴ - 2x³ + 3x² - 5x + 15 - 7

P(x) = x⁴ - 2x³ + 3x² - 5x + 8

Now, When this polynomial is divided by (x + 2), then,x + 2 = 0

x = - 2

∴ P(-2) = (-2)⁴ - 2(-2)³ + 3(-2)² - 5(-2) + 8

⇒ P(-2) = 16 + 16  + 12 + 10 + 8

⇒ P(-2) = 62

Thus, Remainder will be 62.

Answer 2

Answer:

The answer is a = 4/3

Step-by-step explanation:

The zero of the polynomial x +1 is given by

x + 1 = 0

So

x = - 1

f(x) = x⁴ - 2x³+3x² - ax +3a - 7

Now by the Remainder Theorem the Remainder is

Remainder is f(-1)

= (-1)⁴ - 2(-1)³+3(-1)² - a(-1) +3a - 7

= 1 + 2 +3 + a + 3a - 7

= 4a - 1

Again

g(x) = x³ - 4x + a

Now by the Remainder Theorem the Remainder is

g(-1)

= x³ - 4x + a

= (-1)³ - 4(-1) + a

= - 1 + 4 +a

= a + 3

So by the given condition

4a-1 = a + 3

3a = 4

a = 4/3