What are the possible rational roots of 2x^2 - 10x + 8 according to the rational root theorem?
The rational root theorem states that if a polynomial equation has a rational root, then it must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
In this case, the constant term is 8, and the leading coefficient is 2. The factors of 8 are ±1, ±2, ±4, and ±8, and the factors of 2 are ±1 and ±2.
Thus, the possible rational roots of the equation 2x^2 - 10x + 8 are ±1, ±2, ±4, and ±8.
To find the possible rational roots of a polynomial equation, we need to apply the Rational Root Theorem. According to the Rational Root Theorem, if a polynomial equation has a rational root of the form p/q, where p is a factor of the constant term (in this case, 8) and q is a factor of the leading coefficient (in this case, 2), then p/q is a possible rational root of the equation.
Let's find the factors of 8:
Factors of 8 = 1, 2, 4, 8
Let's find the factors of 2:
Factors of 2 = 1, 2
Now, let's form all the possible rational roots by considering the combinations of factors of 8 and factors of 2:
Possible rational roots = ±(1/1), ±(2/1), ±(4/1), ±(8/1)
Simplifying these fractions, we have:
Possible rational roots = ±1, ±2, ±4, ±8
Therefore, the possible rational roots of the equation 2x^2 - 10x + 8, according to the Rational Root Theorem, are ±1, ±2, ±4, and ±8.
To find the possible rational roots of a polynomial equation using the Rational Root Theorem, you need to consider all factors of the constant term divided by all factors of the leading coefficient.
In this case, the given polynomial equation is 2x^2 - 10x + 8.
Step 1: Begin by identifying the constant term and the leading coefficient.
Constant term: 8
Leading coefficient: 2
Step 2: Determine the factors of both the constant term and the leading coefficient.
Factors of 8: 1, 2, 4, 8
Factors of 2: 1, 2
Step 3: Form all possible combinations of the factors by dividing each factor of the constant term by each factor of the leading coefficient.
Possible combinations of factors: ±1/1, ±2/1, ±4/1, ±8/1, ±1/2, ±2/2, ±4/2, ±8/2
Simplifying the fractions, we get: ±1, ±2, ±4, ±8, ±0.5, ±1, ±2, ±4
Therefore, the possible rational roots of the given polynomial equation, according to the Rational Root Theorem, are:
±1, ±2, ±4, ±8, ±0.5