Question

CAN SOMEONE PLEASE HELP ME WITH MY PRE CALCULUS? THANK YOU SM

Answer 1

According to the rational root theorem, if a polynomial

`a_nx^n + a_(n-1)x^(n-1) + \cdots + a_1x + a_0`

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

In this case, we have
`a_n=2` and
`a_0 = 10`, 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)

Answer 2

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

`1`

`2`

`5`

`(5)/(2)`

`10`

Remeber to include the plus and minus sign.