Question

when x³+3x²-mx+4 is divided by x-2 the remainder is m+3. Find the value of m
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Answer 1

SOLUTION

GIVEN

When x³ + 3x²- mx + 4 is divided by x-2 the remainder is m + 3

TO DETERMINE

The value of m

EVALUATION

Let

$\sf{f(x) = {x}^{3} + 3 {x}^{2} - mx + 4}$

$\sf{g(x) = x - 2}$

For Zero of the polynomial g(x) we have

$\sf{g(x) = 0}$

$\implies \sf{x - 2 = 0}$

$\implies \sf{x = 2 }$

So by the Remainder Theorem the required Remainder is

$= \sf{f(2)}$

$\sf{= {(2)}^{3} + 3 \times {(2)}^{2} - 2m + 4}$

$\sf{= 8 + 12 - 2m + 4}$

$\sf{= 24 - 2m }$

So by the given condition

$\sf{m + 3= 24 - 2m }$

$\sf{ \implies \: 3m = 21 }$

$\sf{ \implies \: m = 7 }$

FINAL ANSWER

The required value of m is 7

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