Find the value of \(\displaystyle{f{{\left({0}\right)}}}\), given

Essence Ingram

Essence Ingram

Answered question

2022-04-05

Find the value of f(0), given f(f(x))=0 has roots as 1 & 2, f(x)=x2+αx+β

Answer & Explanation

chambasos6

chambasos6

Beginner2022-04-06Added 12 answers

Step 1
Note that
f(f(x))=(x2+ax+b)2+a(x2+ax+b)+b
Put x=1, x=2 and set to o:
(1+a+b)2+a(1+a+b)+b=0 (1)
(4+2a+b)2+a(4+2a+b)+b=0 (2)
Subtracting first equation from second yields
(a+3)(4a+2b+5)=0
If a=3, then putting value of a in (1) will give a quadratic with no real solutions in b.
So, 4a+2b+5=0
or a=52b4
Putting this value in (1) will lead to b=32
So,
f(0)=b=32

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