Question

Find the value of K , if (x -1) is a factor of 4x^3 + 3x^2- 4x +k.

Answer 1

If (x - 1) is a factor of given polynomial

then, x - 1 = 0 → x = 1 satisfies the given polynomial.

So, put x = 1 ....

4x³ + 3x² - 4x + k = 0

4(1)³ + 3(1)² - 4(1) + k = 0

4 + 3 - 4 + k = 0

Hence, k = -3 ________(Ans.)✓✓

Hope it helps

Answer 2

We have been already told that (x - 1) is a factor of the given polynomial . So , if we find out the value of (x) and then substitute it in the polynomial ; we can find out the value of k.

Value of x :

$\longrightarrow{\tt{x - 1 = 0 }}$

$\longrightarrow{\tt{x = 0 + 1}}$

$\longrightarrow{\tt{x = 1}}$

Thus we have found the value of x being 1 . So , we will go to the next step that is substituting it in the place of x in the polynomial.

Value of polynomial :

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

$\longrightarrow{\tt{p(1) = 4 \times {(1)}^{3} + 3 \times {(1)}^{2} - 4 \times 1 + k}}$

$\longrightarrow{\tt{p(1) = 4 \times 1 + 3 \times 1 - 4 + k}}$

$\longrightarrow{\tt{p(1) = 4 + 3 - 4 + k }}$

$\longrightarrow{\tt{p(1) = 7 - 4 + k }}$

$\longrightarrow{\tt{p(1) = 3 + k}}$

So the value of the polynomial is (3 + k)

Value of k :

In order to find the value of k we will make the polynomial equal to zero. So the same in the form of equation :

$\longrightarrow{\tt{3 + k = 0 }}$

$\longrightarrow{\tt{k = 0 - 3 }}$

$\longrightarrow{\tt{k = -3}}$

$\large{\boxed{\implies{\tt{ k \implies -3}}}}$