factor theorem (1 Viewer)

[ronaldinho]

if constant c is a fraction do u have to do trial and error to get p(x) as 0?

 

[jyu]

if constant c is a fraction do u have to do trial and error to get p(x) as 0?

Yes,

e.g.

p(x) = x^2 +3x/2 +1/2, p(-1) = 0, p(-1/2) = 0.

q(x) = 2x^2 + 3x + 1, q(-1) = 0, q(-1/2) = 0.

q(x) = 2p(x)

Note: The factor theorem is used mainly to find rational factors. There are infinite number of polynomials with irrational factors.

:wave:

 

[ronaldinho]

how i do this?

Prove that the polynomial P(x) = 5x^4 + 2x^3 - 3x^2 - x + 3 does not have integer roots.

what do they mean by....

the zeroes of a polynomial

Prove that P(x).... cannot have rational zeroes...

 

[jyu]

how i do this?

Prove that the polynomial P(x) = 5x^4 + 2x^3 - 3x^2 - x + 3 does not have integer roots.

what do they mean by....

the zeroes of a polynomial

Prove that P(x).... cannot have rational zeros..

Prove that the polynomial P(x) = 5x^4 + 2x^3 - 3x^2 - x + 3 does not have integer roots.

Possible integer roots are +/- 1, +/- 3.
P(+/- 1) =/= 0, P(+/- 3) =/= 0, no integer roots.


zeros of a polynomial and roots of a polynomial are the same.

Prove that P(x).... cannot have rational zeroes

Other possible rational zeros are +/- 1/5, +/- 3/5.
P(+/- 1/5) =/= 0, P(+/- 3/5) =/= 0, no rational zeros.

:wave:

 

[Riviet]

the zeroes of a polynomial

Say x=a is a zero of p(x), then this means that p(a)=0.

Also strictly speaking, polynomials have zeroes while equations have roots.

edit: confused myself =S the above is now correct.

 

[jyu]

Say x=a is a zero of p(x), then this means that p(a)=0.

Also strictly speaking, polynomials have zeroes while equations have roots.

Quote 'Correct. Strictly speaking, equations have solutions, while polynomials have roots.'

Happy 2006 + 1

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