Question

The value of m for which x - 2 is a factor of the
polynomial x4 – x3 + 2x2 - mx + 4 is :-
(A) 10
(B) -10
(C) 4 (D) 9​

Answer 1

GIVEN :

The value of m for which x - 2 is a factor of the

polynomial $x^4 - x^3 + 2x^2 - mx + 4$ is :-

(A) 10

(B) -10

(C) 4

(D) 9​

TO FIND :

The value of m for which x - 2 is a factor of the

polynomial $x^4 - x^3 + 2x^2 - mx + 4$

SOLUTION :

Given polynomial is $x^4 - x^3 + 2x^2 - mx + 4$

Also given that x - 2 is a factor of the  polynomial $x^4 - x^3 + 2x^2 - mx + 4$

i.e; x-2=0

⇒ x=2 is a root of the given polynomial.

Now put x=2 in the given polynomial to get the value of m

$2^4 - 2^3 + 2(2)^2 - m(2) + 4=0$

16-8+8-2m+4=0

20-2m=0

-2m=-20

2m=20

$m=\frac{20}{2}$

⇒ m=10

⇒ option A) 10 is correct.

∴ the value of m is 10 in the given polynomial $x^4 - x^3 + 2x^2 - mx + 4$

Answer 2

Given :- The value of m for which x - 2 is a factor of the

polynomial x⁴ – x³ + 2x² - mx + 4 is :-

(A) 10

(B) -10

(C) 4

(D) 9

Solution :-

we know that, if (x - a) is a factor of polynomial f(x) , than fa) is equal to 0.

given that, x - 2 is a factor of the polynomial x⁴ – x³ + 2x² - mx + 4.

So,

→ x - 2 = 0

→ x = 2 .

Than,

→ f(2) = 0

Putting we get,

→ f(x) = x⁴ – x³ + 2x² - mx + 4 = 0

→ f(2) = (2)⁴ - (2)³ + 2(2)² - 2m + 4 = 0

→ (2)⁴ - (2)³ + 2(2)² - 2m + 4 = 0

→ 16 - 8 + 2*4 - 2m + 4 = 0

→ 8 + 8 - 2m + 4 = 0

→ 16 + 4 - 2m = 0

→ 20 - 2m = 0

→ 2m = 20

dividing both sides by 2,

→ m = 10 (Ans.) (Option A) .

Hence , value of m is 10 for which (x - 2) is factor of given polynomial.

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