Question

the polynomials (2x³-3x²-ax+2) and (2x²-3x²-3x+a) when divided by (x - 2) leave the same reminder. find the value of a​

Answer 1

Step-by-step explanation:

x-2=0

x=2

put in first equation

(2(2)³-3(2)²-2(a)+2

16-12-2a+2

4-2a+2=0

a=3 OK friend

Answer 2

Correct Question :- the polynomials (2x³ + x²-ax+2) and (2x³-3x²-3x+a) when divided by (x - 2) leave the same reminder. find the value of a

Solution :-

when (2x³ + x²-ax+2) divide by (x - 2) remainder is :-

→ f(x) = (2x³ + x²-ax+2)

→ f(2) = 2(2)³ + (2)² - 2a + 2

→ f(2) = 2*8 + *4 - 2a + 2

→ f(2) = 16 + 4 + 2 - 2a

→ f(2) = (22 - 2a)

Similarly, when (2x³-3x²-3x+a) divide by (x - 2) remainder is :-

→ f(x) = (2x³-3x²-3x+a)

→ f(2) = 2(2)³ - 3(2)² - 3*2 + a

→ f(2) = 2*8 - 3*4 - 6 + a

→ f(2) = 16 - 12 - 6 + a

→ f(2) = (a - 2) .

Since remainder is same.

→ 22 - 2a = a - 2

→ 22 + 2 = a + 2a

→ 24 = 3a

→ a = 8 (Ans.)