warm – up #5. homework log fri 1/8 lesson 5 – 4 learning objective: to apply rational zeros...
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Warm – up #51. Find all the zeros of P(x), given is a zero,
Deg = 4 4 roots1+𝑖 −2 1 2
−1+𝑖−2−1
−1−𝑖1−𝑖
1
11+𝑖 −2201−𝑖
00−1
−1+𝑖01
1−𝑖𝑥¿𝑅𝑥2
Warm – up #51. Solve Solve by square root, factoring, or quadratic formula(x – 1)(x + 1) = 0x – 1 = 0x + 1 = 0x = 1 x = –1Or
Homework LogFri
1/8
Lesson 5 – 4
Learning Objective: To apply Rational Zeros Theorem
Hw: #507 Pg. 302 #1 – 19 odd
1/8/16 Lesson 5 – 4 Rational Zeros Day 1
Advanced Math/Trig
Learning Objective To apply the Rational Zeros Theorem
To apply Bound Theorem
Rational Zeros Theorem
Rational #: Quotient of integers , If is a zero of a polynomial with integer coefficients, then p is a factor of the constant term, and q is a factor of the leading coefficient
List all possible rational zeros++…+
Rational Zeros Theorem
q = factors of p = factors of
Possible Rational Zeros = combos
1.
Give the set of possible rational zeros
of P(x)
𝑞=±1 , ±3 𝑝=±1 , ±5 =
, ,
2.
Give the set of possible rational zeros
of P(x)
𝑞=±1𝑝=±1 , ±2 , ±3 ,±6 =
Bounds TheoremUsing synthetic division on poly with real coeff & lead coeff is positive:
(1) If c is a positive real, & all #s in last row are non-negative, c is an upper bound
(no zeros > c)(2) If c is a negative real, & the #s
in last row alternate in sign, c is a lower bound
(no zeros < c)
(0 can be written as +0 or -0)
a) Find smallest possible integer that bounds theorem detects as an upper
bound for the zeros of
13 – 7 15 – 35
32
– 43 – 1
3 3 2 21 28
Stop when neg.
All non-neg.3 is an upper bound
3.
b) Find the negative integer nearest zero that bounds theorem detects as a
lower bound for the zeros of
– 13 – 7 15 – 35
3 – 10 25 – 60 Alt. signs
–1 is a lower bound
3.
Find upper & lower bounds for the zeros
of
11 – 1 – 4 – 2 – 13
1 0 – 42 1 1 – 23 1 2 2 4 – 14 1 3 8 30 107– 1 1 – 2 – 2– 2 1 – 3 2– 3 1 – 4 8 – 26 65
– 6 – 1
4 is upperbound
–3 is lowerbound
Stop when neg.
Stop when not alternating
4.
Find upper & lower bounds for the zeros
of
11 1 – 11 1 – 10
1 2 – 92 1 3 – 53 1 4 1 4 2– 1 1 0 –12– 2 1 – 1 – 9– 3 1 – 2 –5– 4 1 – 3 1 – 3 2
3 is upperbound
– 4 is lowerbound
Stop when neg.
Stop when not alternating
5.
Ticket Out the Door Find upper & lower bounds for the zeros of
Homework#507 Pg. 302 #1 – 19 odd
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