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Student[Calculus1]

  

Roots

  

find the real roots (zeros) of an expression

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Roots(f(x), x, opts)

Roots(f(x), x = a..b, opts)

Roots(f(x), a..b, opts)

Parameters

f(x)

-

algebraic expression or equation in variable 'x'

x

-

name; specify the independent variable

a, b

-

algebraic expressions; specify restricted interval for roots

opts

-

equation(s) of the form numeric=true or false; specify computation options

Description

• 

The Roots(f(x), x) command, where f(x) is an algebraic expression, returns as a list of values points where f(x) is zero.

• 

The Roots(f(x), x = a..b) command, where f(x) is an algebraic expression, returns as a list of values points where f(x) is zero in the interval [a,b].

• 

If f(x) is an equation, this routine finds the roots of the expression lhsfxrhsfx, in the specified interval if one is provided.

• 

If the independent variable can be uniquely determined from the expression, the parameter x need not be included in the calling sequence.

• 

A root (or zero) of f(x) is defined as any point at which the value of the expression f(x) is 0 (zero).

• 

If the expression has an infinite number of roots, a warning message and sample roots are returned.

• 

The opts argument can contain the following equation that sets computation options.

  

 

  

numeric = true or false

  

Whether to use numeric methods (using floating-point computations) to find the roots of the expression. If this option is set to true, the points a and b must be finite and are set to −10 and 10 if they are not provided. The default value of this option is determined by the numeric values in the expression fx: If any of these numeric values is a floating point number (has a decimal point), then this option defaults to to true.  Note: If the numeric option is in effect, then the command does not warn about an infinite number of roots.

Examples

withStudentCalculus1:

Roots3x2x,x

0,13

(1)

Rootssinx,0..10

0,π,2π,3π

(2)

Rootssin1.0x,1..1

−0.3183098862,−0.1591549431,−0.1061032954,−0.07957747155,−0.06366197724,−0.05305164770,−0.03978873577,−0.02448537586,−0.009947183943,0.004973591972,0.01989436789,0.03536776513,0.05305164770,0.06366197724,0.07957747155,0.1061032954,0.1591549431,0.3183098862

(3)

Roots2x3+5x2=4x,x

54574,0,54+574

(4)

Rootsx23x+1x

3252,32+52

(5)

Rootsx23x+1x=0,numeric

0.3819660113,2.618033989

(6)

See Also

Roots

Student

Student[Calculus1]

Student[Calculus1][Asymptotes]

Student[Calculus1][CriticalPoints]

Student[Calculus1][CurveAnalysisTutor]

Student[Calculus1][ExtremePoints]

Student[Calculus1][FunctionChart]

Student[Calculus1][InflectionPoints]

Student[NumericalAnalysis][Roots]