Question

find the value of k if 4x3-2x2+kx+5 leaves remainder -10 when divided by 2x+1? and i want to tell u that after x in the question 3 and 2 is the power of x

Answer 1

let,
$f(x) = 4x^{3}-2 x^{2} + kx +5$

it is divided by 2x+1=0
⇒ value of x=-1/2
(u can find it out by:
 2x+1=0 ∴ x=-1/2
)
remainder=-10
$f(- \frac{1}{2} )=4( - \frac{1}{2}^{3} )-2( - \frac{1}{2})^{2} +k(- \frac{1}{2})+5=-10$

solving the above equation ans is : k=28

Answer 2

$\fontsize{18}{10}{\textup{\textbf{The value of k is 28.}}}$

Step-by-step explanation:  

We have the following theorem :

Remainder Theorem : When a polynomial p(x) is divided by a linear factor (x-a), then the remainder is p(a).

The given polynomial $p(x)=4x^3-2x^2+kx+5$ leaves remainder -10, when divided by 2x+1.

Now,

$2x+1=0\\\\\Rightarrow x=-\dfrac{1}{2}.$

Therefore, we must have

$p(\frac{1}{2})=-10\\\\\Rightarrow 4\times(-\frac{1}{2})^3-2\times(-\frac{1}{2})^2+k\times(-\frac{1}{2})+5=-10\\\\\\\Rightarrow -\dfrac{1}{2}-\dfrac{1}{2}-\dfrac{k}{2}+5=-10\\\\\\\Rightarrow -\dfrac{k}{2}+4=-10\\\\\Rightarrow -\dfrac{k}{2}=--14\\\\\Rightarrow k=28.$

Thus, the required value of k is 28.

Learn more#

Question : Use the remainder theorem to find the value of k,it being given that when $x^3+2x^2+kx+3$ is divided by (x-3),then remainder is 21.

Link : https://brainly.in/question/2469947.