How many times will the digit '1' appear if we write all whole numbers from 1 to 999?
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F(x) = -4x^7 +x^3 -x^2 +5
a) It is a degree 7 polynomial, so will have 7 zeros (some may be repeated).
b) has 3 sign changes, so 1 or 3 positive real zeros. If odd powers have their signs reversed, the signs are changed to +--+, so there are 2 sign changes. There will be 0 or 2 negative real zeros.
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There is actually 1 positive real zero and 0 negative real zeros. This means there are 3 conjugate pairs of complex zeros.
a) It is a degree 7 polynomial, so will have 7 zeros (some may be repeated).
b) has 3 sign changes, so 1 or 3 positive real zeros. If odd powers have their signs reversed, the signs are changed to +--+, so there are 2 sign changes. There will be 0 or 2 negative real zeros.
____
There is actually 1 positive real zero and 0 negative real zeros. This means there are 3 conjugate pairs of complex zeros.