Question

The value of K for which x-1 is a factor of the polynomial 4x^3 + 3x^2 - 4x + K

Answer 1

Answer:

-3

Step-by-step explanation:

$(x - 1) = 0 \\ x = 1$

$x = 1 \: in \: p(x) \\ p(1) = 4 \times {1}^{3} + 3 \times {1}^{2} - 4 \times 1 \\ + k$

$p(1) = 4 + 3 - 4 + k = 0 \\ = 3 + k = 0 \\ k = - 3$

Answer 2

The value of k = - 3

Given :

(x - 1) is a factor of p(x) = 4x³ + 3x² - 4x + k

To find :

The value of k

Solution :

p(x) = 4x³ + 3x² - 4x + k

It is given that (x - 1) is a factor of given polynomial.

Assumption : x = 1

So,

»› 4x³ + 3x² - 4x + k = 0

»› 4 × (1)³ + 3 × (1)² - 4 × 1 + k = 0

»› 4 × 1 + 3 × 1 - 4 × 1 + k = 0

»› 4 + 3 - 4 + k = 0

»› 3 + k = 0

»› k = - 3

• Confirmation :

»› p(x) = 4x³ + 3x² - 4x + k

Let's put value of k in the given polynomial.

»› 4x³ + 3x² - 4x - 3

As given, x = 1

»› 4 × (1)³ + 3 × (1)² - 4 × 1 - 3

»› 4 × 1 + 3 × 1 - 4 × 1 - 3

»› 4 + 3 - 4 - 3

»› 0

Here we get 0.

Hence, value of k = - 3 is correct.