Question

if ( X - 2) is a zero of X cube - 4X square + KX - 8 , find K ​

Answer 1

Answer:

The value of K = 8

Step-by-step explanation:

Given,

(x-2) is a zero of x³ - 4x² + Kx - 8

To find,

The value of k

Solution:

Factor theorem:

p(x) is a polynomial and (x-a) is a linear polynomial. if (x-a) is a factor of p(x), then p(a) = 0

Let us take p(x) = x³ - 4x² + Kx - 8

Since it is given that (x-2) is a zero of p(x), by factor theorem, we have

p(2) = 0

⇒2³ - 4×2² + K×2 - 8 = 0

⇒8 - 16 + 2K - 8 = 0

⇒ - 16 + 2K  = 0

⇒ 2K = 16

⇒ K = 8

∴ The value of K = 8

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Answer 2

Answer:

8 is the required value of 8.

Step-by-step explanation:

Explanation:

Given that, (X - 2) is a zero of $X^3 - 4X^2 + KX - 8$

Now, X - 2 = 0

So, X = 2

As we know that (x-a) is a linear polynomial, and p(x) is a polynomial.

P(a) = 0 if (x-a) is a factor of p(x).

So, let P(X) = $X^3 - 4X^2 + KX - 8$

On putting the value of X = 2 in the equation we get,

⇒ P(X) =  $X^3 - 4X^2 + KX - 8$ = 0

⇒ $(2)^3 - 4(2)^2 + k(2) - 8 = 0$

⇒ 8 - 4 × 4 + 2K - 8 = 0

⇒ -16 + 2K = 0

⇒2K = 16

⇒ K = $\frac{16}{2}$ = 8

Final answer:

Hence, 8 is the required value of K.

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