Question

IF X^4- 2X^3 + 3X^2- AX +B IS A POLYNOMIAL SUCH THAT WHEN IT IS DIVIDED BY X-1 AND X+1 THE REMAINDERS ARE 5 AND 19 RESPECTIVELY. FIND A AND B DETERMINE THE REMAINDER WHEN F(X) IS DIVIDED BY X-2

Answer 1

the value of A= -7-4x/x

Answer 2

Answer : a = 5, b = 8 & Remainder is 10.

Step - by - step explanation :

p(x) = x⁴ - 2x³ + 3x² - ax + b

Keeping value of x = + 1 and x = - 1

p(1) = (1)⁴ - 2(1)³ + 3(1)² - a(1) + b

5 = 1 - 2 + 3 - a + b

5 = 2 - a + b

3 = - a + b _(i)

Similarly, g(x) = x⁴ - 2x³ + 3x² - ax + b

g(-1) = (-1)⁴ - 2(-1)³ + 3(-1)² - a(-1) + b

19 = 1 + 2 + 3 + a + b

13 = a + b _(ii)

By adding (i) and (ii) equation,

16 = 2b

b = 16/2 = 8

Keeping value of b at eq (ii)

13 = a + 8

13 - 8 = 5 = a

So, polynomial is x⁴ - 2x³ + 3x² - (5)x + 8

= x⁴ - 2x³ + 3x² - 5x + 8

Keeping value of x as 2,

f(2) = 2⁴ - 2(2)³ + 3(2)² - 5(2) + 8

= 12 - 10 + 8

= 10