When using the rational root theorem, which of the following is a possible root of the polynomial function below? f(x)=2x^2-4x+9
1 answer:
The only option that meets the root theorem is option b.
<h3>which of the following is a possible root of the polynomial function below?</h3>
The polynomial function is:
The rational root theorem says that if a root is a rational number, then the leading coefficient must be divisible by the denominator of the rational number and the constant term must be divisible by the numerator.
In this case, the constant is 9, and the only option such that the constant is divisible by the numerator is option b: 3
Where 3 is a rational number:
3 = 3/1
The numerator is 3 (which divides 9) and the denominator is 1 (which divides the leading coefficient 9. (notice that it meets the theorem, but it is not an actual root).
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Answer:
M(x₄ ,y₄) = (-3.5 , 0.5) and
N (x₅ ,y₅) = ( -1 , -0.5 )
Step-by-step explanation:
Let the endpoint coordinates for the mid segment of △PQR that is parallel to PQ be
M(x₄ ,y₄) and N(x₅ ,y₅) such that MN || PQ
point P( x₁ , y₁) ≡ ( -3 ,3 )
point Q( x₂ , y₂) ≡ (2 , 1 )
point R( x₂ , y₂) ≡ (-4 , -2)
To Find:
M(x₄ ,y₄) = ? and
N (x₅ ,y₅) = ?
Solution:
We have Mid Point Formula as
As M is the mid point of PR and N is the mid point of RQ so we will have
Substituting the given value in above equation we get
∴
∴
Similarly,
∴
∴
∴ M(x₄ ,y₄) = (-3.5 , 0.5) and
N (x₅ ,y₅) = ( -1 , -0.5 )