Question

If (2x - 1) is a factor of 2x3 + 11x2 + 4x + k, then the value of k is
(0) O
0-5
3
-3​

Answer 1

f(1/2)=2(1/2)³+11(1/2)²+4(1/2)+k=2×1/8+11×1/4+2+k=1/4+11/4+2+k=3+2+k=5+k

5+k=0

or,k= -5

Answer 2

Answer:

-5 is the required value of k.

Step-by-step explanation:

Explanation:

Given in the question, (2x -1 ) is a factor of $2x^3 + 11x^2 + 4x +k$.

Therefore, 2x -1 = 0

⇒2x = 1

⇒x = $\frac{1}{2}$

Step 1:

On putting the value of x in the above polynomial,

⇒$2x^3 + 11x^2 + 4x +k$

⇒ $2 (\frac{1}{2} )^3 + 11(\frac{1}{2} )^2 + 4(\frac{1}{2} ) + k$

⇒$\frac{1}{4} + \frac{11}{4} +2 + k$ = 0

⇒$\frac{ 1+ 11 + 8 + 4k}{4}$ = 0

⇒12 + 8 + 4k = 0

⇒ 20 + 4k = 0

⇒ 4k = -20

⇒ k = -5

Final answer:

Hence, the value of k is -5.

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