Question

Let R1 and R2 be the remainders, when the polynomials x^3 - 2x^2 - 5ax - 7 and x^3 - ax^2 - 12x + 6 are divided by (x + 1) and (x - 2) respectively. If 2R1 + R2 = 6, find the value of a

Answer 1

• x + 1 = 0

=> x = -1

$R_{1}$ = x³ - 2x² - 5ax - 7

=> (-1)³ - 2(-1)² - 5a(-1) - 7

=> - 1 - 2 + 5a - 7

=> 5a - 10 _______ (eq 1)

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• x - 2 = 0

=> x = 2

$R_{2}$ = x³ - ax² - 12x + 6

=> (2)³ - a(2)² - 12(2) + 6

=> 8 - 4a - 24 + 6

=> - 4a - 10 ________ (eq 2)

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• $2R_{1}$ + $R_{2}$ = 6

=> 2(5a + 10) + (- 4a - 10) = 6

=> 10a + 20 - 4a - 10 = 6

=> 6a + 10 = 6

=> 6a = - 4

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a = $\dfrac{-4}{6}$ or $\dfrac{-2}{3}$

___________ [ANSWER]

Answer 2

Answer:

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Step-by-step explanation: