Question

R1 and R2 are the remainder when polynomials (x^3+2x^2-5ax+7) and (x^3+ax^2 -12x+6) are divided by (x+1)and (x-2) respectively. If R1-R2=18.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 - 8 ______ (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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• $R_{1}$ -$R_{1}$ = 18

=> 5a - 8 - (4a - 10) = 18

=> 5a - 8 - 4a + 10 = 18

=> a + 2 = 18

=> a = 18 - 2

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a = 16

____________ [ANSWER]