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4.2 Real Zeros • Finding the real zeros of a polynomial f(x) is the same as solving the related polynomial equation, f(x) = 0. • Zero, solution, root x-intercepts •Rational Zeros: zeros that are rational #’s The Rational Zero Test All possible rational zeros can be r determined by s where • r is the factors of the constant • s is the factors of the coefficient Ex.1 a)Find all possible rational zeros of f(x) = 2x4 + x3 -17x2 – 4x + 6 r= s= b) Determine the rational zeros. Ex. 2 Find all REAL zeros of f(x) = 2x4 + x3 - 17x2 – 4x + 6 Bounds Test: Used to determine which #’s ALL zeros are between • Upper bound – a # 0 that results in the last row in synthetic division being nonnegative. • Lower bound – a # 0 that results in the last row in synthetic division alternating positive and negative. Ex. 3 Find all real zeros of f(x) = x6 + x3 – 7x2 - 3x + 1 a) Find all rational zeros. r= s= b) Use the bounds test to find lower & upper bounds for the zeros. c) Use calculator to approximate the zeros. Ex. 4 Find all real zeros of f(x) = x7 – 6x6 + 9x5 + 7x4 – 28x3 + 33x2 - 36x + 20