Question

find the value of k if x-1 is factor of 4x³ +3x²- 4x + k

Answer 1

x-1 =0
x=1
putting value of x in eqn
4(1)+3(1)-4(1)+k
7-4+k=0
3+k=0
k=-3

Answer 2

Value of k= -3.

Given:

• $4 {x}^{3} + 3 {x}^{2} - 4x + k$

• $x - 1$ is a factor.

To find:

• Find the value of k.

Solution:

Theorem concept to be used:

Factors Theorem: If a polynomial p(x) have a factor x-a, then p(a)=0.

Step 1:

Find value of x from factor.

$x - 1 = 0$

or

$\bf x = 1$

Step 2:

Let

$p(x) = 4 {x}^{3} + 3 {x}^{2} - 4x + k$

Put x= 1 in p(x) and set to zero.

$p(1) = 4 {(1)}^{3} + 3 {(1)}^{2} - 4(1) + k$

or

$4 {(1)}^{3} + 3 {(1)}^{2} - 4(1) + k = 0$

or

$4 + 3 -4 + k = 0$

or

$3 + k = 0$

or

$\bf \pink{k = - 3}$

Thus,

Value of k= -3.

______________________________

Learn more:

1) Find the value of 'a' for which 2x3+ax2+11x+a+3 is exactly divisible by 2x-1

Please show the whole solution also because...

https://brainly.in/question/1194454

2) If x+k is a factor of polynomial x3 + kx2-2x+k+5 then find the value of k

https://brainly.in/question/18689772