Is my work for this problem correct?
Directions: State the possible rational zeros for each function.
Question: f(x) = 3x^2 + 2x – 1
Answer:
Constant term:-1 Factors: 1
Leading coefficient:3 Factors: 1 and 3
±1/1,3= ±1/1,3 and ±1/1,3
= ±1/1 and ±1/3
= ±1 and ±1/3
I don't think so, lets look
3x^2+2x-1=0
x^2+2/3 x =1
x^2+2/3 x +1/9=10/9
(x+1/3)^2= 10/9
x+1/3 = +- 1/3 sqrt 10
x=-1/3 +- 1/3 sqrt10
check that.
Bob, in line #2 , you forgot to divide the 1 by 3
it actually factors into
(x+1)(3x-1) = 0
so x = -1 or x = 1/3
To determine the possible rational zeros for the function f(x) = 3x^2 + 2x - 1, we can use the Rational Root Theorem.
The Rational Root Theorem states that any rational zero of a polynomial with integer coefficients will have a numerator that is a factor of the constant term and a denominator that is a factor of the leading coefficient.
In this case, the constant term is -1 and the leading coefficient is 3.
The factors of -1 are 1 and -1. The factors of 3 are 1 and 3.
So, the possible rational zeros for f(x) are the fractions that can be formed by taking a factor of the constant term divided by a factor of the leading coefficient.
±1 and ±1/3 are the correct possible rational zeros for the given function.
Therefore, your work for this problem is correct.