Question

if the polynomial x^3-ax^2-bx+2 is divided by x-1 and x+2 then the remainder are zero, find the values of a and b​

Answer 1

Step-by-step explanation:

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Answer 2

Concept Introduction: Polynomials are really good.

Given:

We have been Given:

${x}^{3} - a {x}^{2} - bx + 2 = 0$

when divided by

$x - 1 \\ x + 2$

gives remainder zero.

To Find:

We have to Find: Find the values of a and b.

Solution:

According to the problem, putting

$x = 1$

we get,

${1}^{3} - a {1}^{2} - b \times1 + 2 = 0 \\ 1 - a - b + 2 = 0 \\ - b = - 3 + a \\ b = 3 - a$

now putting

$x = - 2$

we get,

${( - 2)}^{3} - a {( - 2)}^{2} - b \times - 2 + 2 \\ - 8 - 4a + 2b + 2 = 0 \\ 2b = 8 - 2 + 4a \\ 2b = 6 + 4a \\ b = 3 + 2a$

now equating both the equations we get,

$3 - a = 3 - 2a \\ a = 0$

therefore,

$b = 3 - a \\ b = 3$

Final Answer: The values are

$a = 0 \\ b = 3$

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