Question

we get the same remainder if polynomial x³ + x²- 4 x + a and 2x³ + ax² + 3 x - 3 are divided by x - 2 find value of a

Answer 1

Heya !!!

( X - 2 ) is a common factor of the given two polynomials.


So,


( X - 2 ) = 0


X = 2


P1(X) = X³+X²-4X+a


P1(2) = (2)³ + (2)² - 4 × 2 + a



=> 8+4-8+a


=> 4+a


P2(X) = 2X³+AX²+3X-3


P2(2) = 2 × (2)³ + A × (2)² + 3 × 2 - 3


=> 16 + 4A + 6 - 3



=> 4A + 19



According to question,


Polynomials p1(X) and P2(X) when divided by ( x - 2 ) gives same remainder.


So,


(4+A ) = ( 4A + 19)



4A - A = -19+4



3A = -15


A = -15/3 = -5

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★ HOPE IT WILL HELP YOU ★

Answer 2

Hey!!

( x - 2 ) is a factor of common factor of the two given polynomial

( x - 2 ) = 0

=> x = 2

p ( x ) = x^3 + x^2 - 4x + a

=> p1 ( 2 ) = ( 2 )^3 + ( 2 )^2 - 4( 2 ) + a

=> 0 = 8 + 4 - 8 + a

=> 4 + a

And,

p2 ( x ) = 2x³ + ax² + 3 x - 3

=> p ( 2 ) = 2( 2 )^3 + a( 2 )^2 + 3 (2) - 3

=> 0 = 16 + 4a + 3

=> 19 + 4a

A/q

p1 (x) and p2 ( x ) are divided by ( x - 2 ) it gives remainder,

4 + a = 19 + 4a

=> a - 4a = 19 - 4

=> - 3a = 15

=> a = - 15 / 3

=> a = - 5 >>>> Answer

Therefore the value of a is - 5

Hope it will helps you ✌