SOLVING POLYNOMIAL EQUATIONS

Determining the Real Roots of an Equation

is equivalent to

Determining the x-coords of the PoIs of 2 Functions

which is also equivalent to

Determining the Zeros of a Combined Function

REAL ROOTS OF EQN = X-COORDS OF POIS = ZEROS OF FN

x

y

x

y

REAL ROOTS OF EQN = X-COORDS OF PoIs = ZEROS OF FN

-5 -4 -3 -2 -1 1 2 3 4 5

-10

10

20

30

40

50

60

x

y

A polynomial equation of degree “n” has “n” complex roots but will have AT MOST “n” real roots!

REAL ROOTS OF EQN = X-COORDS OF POIS = ZEROS OF FN

Complex roots may be all real (“a”) or all imaginary (“± bi”) or a mixture (“a ± bi”).

REAL ROOTS OF EQN = X-COORDS OF PoIs = ZEROS OF FN

xx 284 3 234 13544 xxxx Ex#3] Ex#4]0284 3 xx

074 2 xx0x or 72 x

7x the real roots are

7,0,7

051344 234 xxxx0)51344( 23 xxxx

0x or 051344 23 xxx51344)( 23 xxxxhLet

factoraisxh )1(0)1(

0584

584

513441

05841 2 xxx 0)52(121 xxx

25

211 xorxorx

the real roots are 1,,0, 21

25