Respuesta :

Step-by-step explanation:

Apply Rational Root Thereom:

If we have a polynomial, P(x), the possible roots of the polynomial are the factors of the constant divided by the factors of the leading coeffceint.

Our constant is 10 and our leading coefficient is 2 so our possible factors are (the factors are positive and negative).

10:1,2,5,10

2:1,2

So our possible roots are

[tex]1[/tex]

[tex]2[/tex]

[tex]5[/tex]

[tex] \frac{5}{2} [/tex]

[tex]10[/tex]

Remeber to include the plus and minus sign.

LammettHash

According to the rational root theorem, if a polynomial

[tex]a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0[/tex]

has any rational roots, they take the form of ± (some divisor of [tex]a_0[/tex], the constant term) divided by (some divisor of [tex]a_n[/tex], the coefficient of the leading term).

In this case, we have [tex]a_n=2[/tex] and [tex]a_0 = 10[/tex], which have divisors

• 2: 1, 2

• 10: 1, 2, 5, 10

Then the possible candidates for rational roots are

±1/1 = ±1

±2/1 = ±2

±5/1 = ±5

±10/1 = ±10

±1/2

±2/2 = ±1 (already accounted for)

±5/2

±10/2 = ±5 (already accounted for)

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