Question

4) If both ax3+2x2-3 and x2 - ax +4 leave the same
remainder when divided by X-2, find a​

Answer 1

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Answer 2

The value of a = 3/10

Given:

ax³+2x²- 3 and x² - ax +4 are leaves same remainder when divided by x-2

To find:

The value of a

Solution:

Let the given equations

f(x) = ax³+2x²- 3

g(x) = x² - ax +4          

Note: when a polynomial p(x) is divided by (x-a) then the remainder will be equals to p(a)

Given that f(x) and g(x) are divided (x-2)

The remainder when f(x) is divided by (x -2)

=> f(2) = a(2³)+2(2²)- 3 = 8a + 8 - 3 = 8a + 5

=> f(2) = 8a + 5

The remainder when g(x) is divided by (x -2)

=> g(2) = (2²) - a(2) + 4 = 4 - 2a + 4 = -2a + 8

=> g(2) = -2a + 8  

From given data f(2) = g(2)

⇒ 8a + 5 = -2a + 8

⇒ 10a = 3

⇒ a = 3/10  

Therefore,

The value of a = 3/10

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