Question

LET R1 AND R2 ARE THE REMINDERS WHEN THE POLYNOMIAL X³+2X²-5AX-7 AND X³+AX²-12X+6 ARE DIVIDEND BY (X+1) AND (X-2) RESPECTIVELY Y 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 - 6 ________ (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 - 6) + 4a - 10 = 6

=> 10a - 12 + 4a - 10 = 6

=> 14a = 6 + 22

=> 14a = 28

=> a = $\dfrac{28}{14}$

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a = 2

__________ [ANSWER]