Question

The value of K for which ( x -1) is a factor of the polynomial 4x³ + 3x² - 4x + k is : ?

Answer 1

Answer:

Step-by-step explanation:

x-1=0

x=1

substitute

4x^3 +3x^2-4x+k=0

4(1)^3+3(1)^2-4(1)=-k

4+3-4=-k

3=-k

k=-3

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Answer 2

$\large\bf\underline {To \: find:-}$

• We need to find the value of K

$\large\bf\underline{Given:-}$

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

$\huge\bf\underline{Solution:-}$

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

putting value of x = 1 in the given polynomial.

➛ 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

❥ Verification :-

➛p(x) = 4x³ + 3x² - 4x + k

putting value of k in the given polynomial.

➛ 4x³ + 3x² - 4x - 3

• x = 1 [ Given ]

➛ 4 × (1)³ + 3 × (1)² - 4 × 1 - 3

➛ 4 × 1 + 3 × 1 - 4 × 1 - 3

➛ 4 + 3 - 4 - 3

➛ 0

Hence, we get 0.

So, value of k = -3 is correct.

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