The polynomials ax ³ +3x³and 2x³-5x+a when divided by (x-4)leaves the remainder k1 and k2 respectivley dind the value of a if k1 + k2=0
Answers
Given :
The first polynomial = a x³ + 3 x² - 3
The remainder of first polynomial =
The second polynomial = 2 x³ - 5 x + a
The remainder of first polynomial =
Both the polynomials are divided by ( x - 4 )
The sum +
= 0
To Find :
The value of a
Solution :
∵ Both the polynomials are divided by ( x - 4 )
So, It must satisfy the polynomials ,
i.e x = 4
So, Put the value of x in both polynomials
Or, a x³ + 3 x² - 3 = a × (4 )³ + 3 × (4 )² - 3
= 64 a + 48 - 3
= 64 a + 45
And
2 x³ - 5 x + a = 2 × (4 )³ - 5 × 4 + a
= 128 - 20 + a
= 108 + a
∵ The sum of remainder of both polynomials = 0
i.e +
= 0
So, ( 64 a + 45 ) = ( 108 + a )
Or, ( 64 a - a ) = ( - 45 + 108 )
Or, 63 a = 63
∴ a =
i.e a = 1