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Find the values of a and b such that x^4 +ax^3 -7x^2 - 8x +b is exactly divisible by(x+2) and (x+3)

User Thephatp
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1 Answer

3 votes

Answer:

a = 2 ; b = 12

Explanation:

p(x)=x⁴ + ax³ - 7x² - 8x +b

p(x) is exactly divisible by (x + 2). So p(-2)=0

(-2)⁴ + a(-2)³ - 7(-2)² - 8(-2) +b = 0

16 - 8a - 7*4 +16 + b =0

16 - 8a - 28 + 16 + b =0

4 - 8a + b = 0

-8a + b = -4 -----------(i)

p(x) is exactly divisible by (x + 3). So p(-3)=0

(-3)⁴ + a(-3)³ - 7(-3)² - 8(-3) +b = 0

81 -27a - 63 + 24 + b =0

42 - 27a + b = 0

-27a + b = -42 ------------(ii)

-8a + b = -4 -----------(i)

-27a + b = -42 ------------(ii)

subtract 19a = 38

a = 38/19 = 2

a=2

Substitute a value in equation (i)

-8*2 + b= -4

-16 + b = -4

b = -4 + 16

b = 12

User Ralitza
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