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Chapter 4: Q. 88 (page 210)

Find k such that f(x)=x4-kx3+kx2+1has the factorx+2.

Short Answer

Expert verified

The required value of k is -1712.

Step by step solution

01

Step 1. Concept Used 

The factor theorem states that iff is a polynomial function, then x-cis a factor of f if and only if f(c)=0.

02

Step 2. Form an equation 

As it is given thatx+2 is a factor of f(x)=x4-kx3+kx2+1.

So by the factor theorem we have f(-2)=0.

f(-2)=0(-2)4-k(-2)3+k(-2)2+1=016+8k+4k+1=017+12k=0

03

Step 3. Solve the equation 

In the equation subtract 17from both sides

17+12k-17=0-1712k=-17

Now divide both sides by 12 and solve for k.

12k12=-1712k=-1712

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