Range of k for roots of \(\displaystyle{\left|{x}^{{{2}}}-{1}\right|}+{x}^{{{2}}}+{k}{x}={0}\) lying

David Rodgers

David Rodgers

Answered question

2022-04-02

Range of k for roots of |x21|+x2+kx=0
lying between (0, 2)

Answer & Explanation

Brennan Thompson

Brennan Thompson

Beginner2022-04-03Added 10 answers

Step 1
|x21|+x2+kx=kx+1 when x[1,1]
If k1 we have one root in (0, 1]
Now we need to find the range of k such that.
2x2+kx1 has a root in (1, 2)
1<k+k2+84
4+k<k2+8
16+8k+k2<k2+8
k<1
And
2>k+k2+84
8+k>k2+8
64+16k+k2>k2+8
16k>56
k>72

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