the polynomials p(x)= ax^3 + 3x^2 - 13 , g(x)=2x^3-15x+a are divided by x+2 and if the remainder in each case is the same, find value of a.
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= > x + 2 = 0
= > x = - 2
Given that it leaves the same reminder , so
= > p( - 2 ) = g( - 2 )
= > a( - 2 )³ + 3( - 2 )² - 13 = 2( - 2 )³ - 15( - 2 ) + a
= > - 8a + 12 - 13 = - 16 + 30 + a
= > - 8a - 1 = 14 + a
= > - 14 - 1 = 8a + a
= > - 15 = 9a
= > - 15 / 9 = a
= > - 5 / 3 = a
Therefore, value of x is -5 /3
= > x = - 2
Given that it leaves the same reminder , so
= > p( - 2 ) = g( - 2 )
= > a( - 2 )³ + 3( - 2 )² - 13 = 2( - 2 )³ - 15( - 2 ) + a
= > - 8a + 12 - 13 = - 16 + 30 + a
= > - 8a - 1 = 14 + a
= > - 14 - 1 = 8a + a
= > - 15 = 9a
= > - 15 / 9 = a
= > - 5 / 3 = a
Therefore, value of x is -5 /3
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