Question

pleaseee solve questions no 9 pleaseee fast

Answer 1

Answer:

5,8

Step-by-step explanation:

Remainder theorem: If a polynomial f(x) is divided by (x - a), remainder is f(a).

Given Equation is x⁴ - 2x³ + 3x² - ax + b.

When f(x) is divided by (x - 1), the remainder is f(1) = 5{Given}.

∴ f(1) = 1⁴ - 2(1)³ + 3(1)² - a(1) + b

⇒ 5  = 1 - 2 + 3 - a + b

⇒ -a + b = 3    ------ (i)

Given that f(x) is divided by f(x + 1), the remainder is 19.

∴ f(-1) = (-1)⁴ - 2(-1)³ + 3(-1)² - a(-1) + b

⇒ 19 = 1 + 2 + 3 + a + b

⇒ a + b = 13     ------ (ii)

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

-a + b = 3

a + b = 13

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

2b = 16

b = 8.

Substitute b = 8 in (i), we get

a + b = 13

a + 8 = 13

a = 5

Therefore, the values of a and b are 5,8

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