Download Section 3.3 Real Zeroes of Polynomials Rational Zeroes Theorem

Section 3.3 ­ Real Zeroes of Polynomials
Rational Zeroes Theorem (Rational Root Theorem)
If the polynomial has integer coefficients, then every p
rational zero is of the form q
where p is a factor of the constant
and q is a factor of the leading coefficient
Sep 30­7:11 AM
1
Finding the rational zeroes of a polynomial
1. List all possible rational zeroes using the rational root theorem
2. Use synthetic division to evaluate the polynomial at the possible rational roots. When the remainder is 0, you found a root. Use the calculator to help you narrow the possibilities. (The quotient is called the depressed equation)
3. Repeat step 2 to the previous quotient until you have reached a quadratic polynomial.
4. Solve the quadratic polynomial by factoring, quadratic formula or completing the square.
Sep 30­7:14 AM
2
Oct 20­11:35 AM
3
Descartes' Rule of Signs
If P is a polynomial with real coefficients
1. The number of positive real roots is either equal to the number of variations in the sign of P(x) or is less by an even whole number.
2. The number of negative real roots is either equal to the number of variations in the sign of P(­x) or is less by an even whole number.
Sep 30­7:19 AM
4
Oct 20­11:43 AM
5