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Polynomials question! (1 Viewer)
- Thread starter moivre
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It's monic so you know that the leading coeficient is 1. Hence the factors are going to be in the form (x - r)
[ok... so you could have (1/2x - r)(2x-q) but we'll ignore that for simplicity's sake]
You can pretty much assume that the P(x) = (x - 5)(x + 2)(x + 2) since 5 is a single zero and -2 is a zero of multiplicity two. EDIT: From the factor theorem you know that if P(r)=0 then (x - r) is a factor.
so P(x) = x<sup>3</sup> - x<sup>2</sup> - 16x - 20
[ok... so you could have (1/2x - r)(2x-q) but we'll ignore that for simplicity's sake]
You can pretty much assume that the P(x) = (x - 5)(x + 2)(x + 2) since 5 is a single zero and -2 is a zero of multiplicity two. EDIT: From the factor theorem you know that if P(r)=0 then (x - r) is a factor.
so P(x) = x<sup>3</sup> - x<sup>2</sup> - 16x - 20
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From the factor theorem we know that if P(γ )=0 i.e if we sub in γ for x then P(x) reduces to zero then we know that (x-γ ) is a factor of P(x) so that P(x) can be expressed as:
P(x) = (x - γ ).Q(x)
since we know that 5 is s single zero i.e P(5)=0 ------> (x-5) is a factor of P(x)
We know that P(-2)=0 and we're told that '-2' is a zero of multiplicity two i.e it is a double root (where the graph bounces off of the x-axis like in y=x<sup>2</sup>) so we can conclude that (x + 2)(x +2) = (x +2)<sup>2</sup> is a factor.
Since P(x) is a monic of degree three we can figure that those are the three factors which make up the polynomial.
i.e P(x)= (x - 5)(x +2)(x +2)
[Anyone correct me if I assume too much
)
P(x) = (x - γ ).Q(x)
since we know that 5 is s single zero i.e P(5)=0 ------> (x-5) is a factor of P(x)
We know that P(-2)=0 and we're told that '-2' is a zero of multiplicity two i.e it is a double root (where the graph bounces off of the x-axis like in y=x<sup>2</sup>) so we can conclude that (x + 2)(x +2) = (x +2)<sup>2</sup> is a factor.
Since P(x) is a monic of degree three we can figure that those are the three factors which make up the polynomial.
i.e P(x)= (x - 5)(x +2)(x +2)
[Anyone correct me if I assume too much
)
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