Question

Find the value of k if x3-6x2+kx+6 is divided by x-2 and gives remainder 12

Answer 1

Reqd. equation

$f(2) = 12 \\ = > 8 - 24 + 2k + 6 = 12 \\ = > - 10 + 2k = 12 \\ = > k = \frac{22}{2} = 11$

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Answer 2

The value of k is 11.

Step-by-step explanation:

Since we have given that

$f(x)=x^3-6x^2+kx+6$

When it is divided by (x-2), the remainder is 12.

So, we get that

$x-2=0\\\\x=2\\\\f(2)=(2)^3-6\times (2)^2+2k+6\\\\12=8-24+2k+6\\\\12=-16+6+2k\\\\12=-10+2k\\\\12+10=2k\\\\22=2k\\\\k=\dfrac{22}{2}\\\\k=11$

Hence, the value of k is 11.

# learn more:

When ( x3 + 3x2 – kx + 4) is divided by (x-2), the remainder is k, Find the value

of k.

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