5'6: Polynomial Equations

1
5.6 Polynomial Equations

• Quadratic Eqns
• Higher Degree Eqns
• Eqns in quadratic form
• Applications

2
Solving a Quadratic Eqn

• Solve symbolically x2 - 4 0
• Since the eqn consists of a factorable polynomial
  on one side and 0 on the other, we can use the
  zero-product property
• x2 - 4 0
• (x-2)(x2) 0
• X-2 0 or x2 0
• X -2 or x 2

3
Solve 3x2 11x 20

• Re-write to get a quadratic on one side and zero
  on the other .
• 3x2 11x - 20 0
• Now factor and use zpp

4
Solve 3x2 11x 20 graphically

• Enter 3x2 11x - 20 in Y1 and graph
• Use the Calc feature to find the zeros or
  x-intercepts.

5
Solve symbolically 16x4 - 64x3 64x2 0

• Factor out GCF
• 16x2(x2 - 4x 4) 0
• Factor the trinomial a PST?
• x2 - 4x 4 (x - 2)2
• 16x2(x - 2)2 0 apply ZPP

(x - 2)(x-2) 0 x 2
16x2 0 x2 0 x 0
6
Solve graphically 16x4 - 64x3 64x2 0

• Enter lse in Y1 rse in Y2
• GRAPH
• Adjust Window if necessary to see where graphs
  intersect
• CALC the Intersection of the 2 graphs using
  method previously discusssed.

7
5.6 Homework

• 13 - 16
• 25 - 26
• 33 - 36