Question

if the polynomial ax^3+3x^2-13 and 2x^3-5x+a when divided by x-2 leave the same remainder, find the value of a

Answer 1

Hey !!




X - 2 = 0


X = 2



P(X ) = AX³ + 3X² - 13



P(2) = A × (2)³ + 3 × (2)² - 13




=> 8A + 12 - 13




=> 8A - 1








P1(X ) = 2X³ - 5X + A



P1(2) = 2 × (2)³ - 5 × 2 + A





=> 16 - 10 + A



=> A + 6





According to the question , when polynomial ax² + 3x² - 13 and 2x³ - 5x + a is divided by ( x - 2 ) , then remainder of both the polynomial will be equal.



So,


8a - 1 = a + 6




8a - a = 7



7a = 7



a = 7/7



a = 1