Because f(a_1)= f(a_2)= f(a-3) = f(a_4) = f(a_5) = 2
So defining g(x) = f(x) - 2
We get g(a_1)= g(a_2)= g(a-3) = g(a_4) = g(a_5) = 0
So g(x) = (x-a_1)(x-a_2)(x-a_3)x-a_4)(x-a_5)h(x) for some function h(x) of x
So g(x) is product of atleast 5 different numbers
Because f(b) = 9 so g(b) = 7
For g(x) to be 7 at some b 7 should be product of 5 different numbers but is is not product of have at least 5 different factors but 7 has at most 3(as -7 * -1 * 1) so it is not possible for any b such that g(b) = 7 or f(b) = 9
2 comments:
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Thanks for your comments. I do not make any money from the blog
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