Question

When x³ − 2x² + 6x − k is divided by x − 2, the remainder is −10. The value of k is ______.

पर्याय

• 20

• −20

• 22

• −22

Answer 1

When x³ − 2x² + 6x − k is divided by x − 2, the remainder is −10. The value of k is 22.

Explanation:

Let f(x) = x³ − 2x² + 6x − k

Now, by the remainder theorem,

f(2) = −10

Step 1: Substitute x = 2 in f(x)

f(2) = 2³ − 2(2)² + 6(2) − k

= 8 − 2(4) + 6(2) − k

= 8 − 8 + 12 − k

= 12 − k

Step 2: Set equal to the remainder

12 − k = −10

Step 3: Solve for k

12 − k = −10

−k = −10 − 12

−k = −22

k = 22