Given quadratic equation: \(\displaystyle{7}{x}^{{2}}-{\left({k}+{13}\right)}{x}+{k}^{{2}}-{k}-{2}={0}\), where k is

aidinacol7

aidinacol7

Answered question

2022-03-25

Given quadratic equation:
7x2(k+13)x+k2k2=0, where k is a constant, has two distinct real roots α and β. Given that 0<α<1 and 1<β<2, find the range of values of k.

Answer & Explanation

Cindy Reynolds

Cindy Reynolds

Beginner2022-03-26Added 7 answers

Let f(x)=7x2(k+13)x+k2k2..
Now, solve the following system.
f(0)>0,
f(1)<0
and f(2)>0
which is k2k2>0
k22k8<0
and k23k>0

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