Question

if (x-1) is a factor of 4x². +3x²-4x+k then find the value of k​

Answer 1

Step by step explanation:-

Given:-

$(x - 1) \: is \: a \: factor \: for \: 4x {}^{3} + 3x {}^{2} - 4x + k$

To find :-

$value \: of \: k$

Solution:-

Since x-1 is a factor If we Substitute x value Then it should be equal to 0 From this we can find value of k

$x - 1 = 0$

$x = 1$

Substitute x value in given equation

$4x {}^{3} + 3x {}^{2} - 4x + k$

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

$4 + 3 - 4 + k = 0$

$7 - 4 + k =$

$3 + k = 0$

$k = \: - 3$

So, the value of k is -3

Verification:-

Substitute value of x, k in given equation It should be equal to 0

$4x {}^{3} + 3x {}^{2} - 4x + k$

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

$4 + 3 -4 -3=$

$7 -7 = 0$

0 = 0

LHS = RHS

Verified !