Question

If the polynomials 2x³+ax+3x-5and x³+x²-4x++a leave the same remainder when divided by x-2,find the value of a​

Answer 1

Correct question:

If the polynomials 2x³+ax²+3x-5and x³+x²-4x+a leave the same remainder when divided by x-2,find the value of a

Solution:

g(x) = x - 2 = 0

=> x = 2

p(x) = 2x³ + ax² + 3x - 5

p(2) = 2(2)³ + a(2)² + 3(2) - 5

Remainder = 16 + 4a + 6 - 5

Remainder = 17 + 4a

p(x) = x³ + x² - 4x + a

p(2) = (2)³ + (2)² - 4(2) + a

Remainder = 8 + 4 - 8 + a

Remainder = 4 + a

Both these remainders are equal. Thus:

17 + 4a = 4 + a

=> 13 = 3a

=> a = 13/3

Answer 2

Solutions:

f(x) = x - 2 = 0

= 2

g(x) = x³ + x² - 4x + a

= (2)² + (2) - 4(2) + a

= 8 + 4 - 8 + a

=

g(x) = 2x³ + ax² + 3x - 5

= 2(2)³ + a(2)² + 3(2) - 5

= 16 + 4a + 6 - 5

= 17 + 4a

17 + 4a = 4 + a

17 - 4 = a - 4a

-3a = 13

a = -13/3

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