Answer :
The real zeros of the polynomial f(x)=4x^4-8x^3-19x^2+23x-6 are 1, -1/2, 3/2, and 2.
The real zeros of the polynomial f(x)=4x4-8x3-19x2+23x-6 can be found by factoring the polynomial or by using the Rational Zero Theorem.
When we factor the polynomial, we get f(x)=(x-1)(2x+1)(2x-3)(x-2). So, the real zeros of the polynomial are x = 1, x = -1/2, x = 3/2, and x = 2.
The Rational Zero Theorem can also be used to find the real zeros of the polynomial. According to the theorem, the potential rational zeros of the polynomial are the factors of the constant term (6) divided by the factors of the leading coefficient (4). After trying out these potential zeros, we find that they indeed correspond to the real zeros of the polynomial.
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