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Descartes’  rule of signs:

f(x) has 2 changes of sign, implying at most two positive zeroes.

f(-x)=3x⁴+5x³-x²+8x+4 has 2 changes of sign, implying at most two negative zeroes.

The degree of f(x) is 4, so the number of complex zeroes could be 4-(2+2)=0.

In actual fact, there are 2 complex zeroes and two real positive zeroes.

Complex zeroes always come in conjugate pairs, so in this case there are none, 2 or 4. With two positive zeroes we have 2 negative zeroes or 2 complex zeroes.

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