Question

find the value of K so that (2x-1) is a factor of 8x power 4 + 4x Power 3 - 16x power 2 + 10x +K​

Answer 1

Given

we have given 2x-1 is a factor of 8x⁴+4x³-16x²+10x+k

To find

We have to find the value of x

$\sf\huge {\underline{\underline{{Solution}}}}$

Since , 2x-1 is a factor of 8x⁴+4x³-16x²+10x+k

Make equal to zero,we get

x= 1/2

Let f(x) = 8x⁴+4x³-16x²+10x+k

Now, put x in f(x)

=> f(1/2) = 8(1/2)⁴+4(1/2)³-16(1/2)²+10(1/2)+k

=>f(1/2)= 8*1/16+ 4*1/8-16*1/4+10/2+k

=> f(1/2)= 1/2+1/2-4+5+k

=> f(1/2)= 1+1+k= 2+k

Now , makes equal to zero to find out the value of k

=> k+2=0

k= -2

Hence,value of k is -2

Answer 2

Step-by-step explanation:

Given

we have given 2x-1 is a factor of 8x⁴+4x³-16x²+10x+k

To find

We have to find the value of x

\sf\huge {\underline{\underline{{Solution}}}}

Solution

Since , 2x-1 is a factor of 8x⁴+4x³-16x²+10x+k

Make equal to zero,we get

x= 1/2

Let f(x) = 8x⁴+4x³-16x²+10x+k

Now, put x in f(x)

=> f(1/2) = 8(1/2)⁴+4(1/2)³-16(1/2)²+10(1/2)+k

=>f(1/2)= 8*1/16+ 4*1/8-16*1/4+10/2+k

=> f(1/2)= 1/2+1/2-4+5+k

=> f(1/2)= 1+1+k= 2+k

Now , makes equal to zero to find out the value of k

=> k+2=0

k= -2

Hence,value of k is -2