1.

The polynomial p(x) = x^4-2x^3 + 3x^2-ax+3a-7 when divided by x + 1 leaves the remainder 19. Findthe values of a. Also find the remainder when p(x) is divided by x + 2.​

Answer»

Answer:

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.


Discussion

No Comment Found

Related InterviewSolutions