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x^4-2ax^2+x+a^2-a find the value of a for which all its roots are real

x^4-2ax^2+x+a^2-a find the value of a for which all its roots are real

Grade:11

1 Answers

Vikas TU
14149 Points
7 years ago
let x^2 = t then t >=0
then 
t^2 – 2at + a^2 – a =0
For Real Roots,
 
D>=0
4a^2 -4(a^2 -a) >=0
a>=0
 
The roots in terms of a are:
t1 = a + root(a) > 0
and 
t2 = a – root(a) > 0
 

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