Question

if x-1 is a factor of the polynomial x2-k÷2x+4,then the value of k is​

Answer 1

Answer:

x-1=0 so, x=1

put the value of x in given polynomial

x2-k÷2x+4=0

putting the value of x

(1)^2 -k ÷ 2x1 +4=0

1-k ÷6=0

1-k=0x6

1-k=0

k=1 hence

value of k is 1

Answer 2

SOLUTION

GIVEN

x-1 is a factor of the polynomial

$\displaystyle \sf{ {x}^{2} - \frac{k}{2} \: x + 4 }$

TO DETERMINE

The value of k

EVALUATION

Let

$\sf{f(x) = x - 1}$

$\displaystyle \sf{ g(x) = {x}^{2} - \frac{k}{2} \: x + 4 }$

For Zero of the polynomial f(x) we have

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

$\implies \sf{x - 1 = 0}$

$\implies \sf{x = 1 }$

So by the Remainder Theorem the required Remainder is

$\displaystyle \sf{ = g(1) }$

$\displaystyle \sf{ = {(1)}^{2} - \bigg( \frac{k}{2} \times 1 \bigg) + 4 }$

$\displaystyle \sf{ = 1- \bigg( \frac{k}{2} \times 1 \bigg) + 4 }$

$\displaystyle \sf{ = 5 - \frac{k}{2} }$

Since x - 1 is a factor of g(x)

∴ Remainder = 0

$\displaystyle \sf{ \implies \: \displaystyle \sf{ g(1) = 0}}$

$\displaystyle \sf{ \implies \: \displaystyle \sf{ 5 - \frac{k}{2} = 0 }}$

$\displaystyle \sf{ \implies \: \displaystyle \sf{ \frac{k}{2} = 5 }}$

$\displaystyle \sf{ \implies \: \displaystyle \sf{ k = 10 }}$

FINAL ANSWER

Hence the required value of k is 10

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