Question

the polynomials (2x cube + x square - ax + 2) and (2x cube - 3x square - 3x + a) when divided by (x-2) leave the same remainder.find the value of a.

Answer 1

put x= 2 in both equations and equate them
$2( {2}^{3} ) + {2}^{2} - 2a + 2 = \\ \: \: \: \: \: \: 2( {2})^{3} - 3 ({2})^{2} - 6 + a \\ 16 + 4 + 2 - 2a = 16 - 18 - 6 + a \\ 22 - 2a = - 8 + a \\ - 2a - a = - 8 - 22 \\ - 3a = - 30 \\ a = \frac{30}{3} = 10 \: \: \: \: \: \: ans$

Answer 2

Answer:

Value of a is 8.

Step-by-step explanation:

let, p(x) = 2x³ + x² - ax + 2

g(x) = 2x³ - 3x² - 3x + a

To find : Value of a when p(x) & g(x) divided by x - 2 leaves the same remainder.

We use remainder theorem,

Remainder Theorem states that When a polynomial p(x) is divided by a  polynomial x - a then the remainder is p(a).

So, Remainder when p(x)  divided by x - 2

Remainder we get ,

p(2) = 2(2)³ + (2)² - a(2) + 2

= 2 × 8 + 4 - 2a + 2

= 22 - 2a ...............(1)

Remainder when g(x)is divided by x - 2

g(2) = 2(2)³ - 3(2)² - 3(2) + a

= 2 × 8 - 3 × 4 - 6 + a

= a - 2 .........................(2)

We are given (1) = (2)

p(2) = g(2)

22 - 2a = a - 2

3a = 24

a = 8

Therefore, Value of a is 8.