Introduction to possible rational zeros:
All polynomials in one variable of degree n, n > 0, has at least one real or complex zero. This is the Fundamental Theorem of Algebra.To find all the possible rational zeros of a polynomial we use the Rational Root Test. Understanding Properties of Rational Exponents is always challenging for me but thanks to all math help websites to help me out.
Problems on Rational Root Test:
If a polynomial function has integer coefficients, then all the rational zeros will be of the form p/q where p is a factor of the constant and q is a factor of the leading coefficient.
Lets look at a few examples.
Ex 1: Find all the possible rational zeros of 2`x^(2)` + 6x +4
Here p = 4 and q = 2
The factors of 4 are 4,2 and 1
similarly the factors of 2 are 2 and 1
So all the possible rational zeros will be of the form : `( +-4, +-2, +-1)/( +-2, +-1)`
Now let us list out all the possible rational zeros: 4, 2, -4, -2, 1, -1, `(1)/(2)` , `(-1)/(2)` .
Ex 2: Find all the possible rational zeros of 2`x^(4)` - 7`x^(3)` +3x + 6.
Here p = 6. The factors of 6 are 3, 2, 1
q = 2. The factors of 2 are 2,1
So all the possible rational zeros will be of the form :`( +-3, +-2, +-1)/( +-2, +-1)`
Therefore the possible rational zeros are :
` ( 3)/(2)` , `(-3)/(2)` , 3, -3, 2, -2, 1, -1, `(1)/(2)` , `(-1)/(2)`
Is this topic how to calculate p value hard for you? Watch out for my coming posts.
Things that we should be Careful while Applying the Rational Root Test:
Always make sure the polynomial has integer coefficients. We have to multiply to get rid of fractions or decimals and later divide by the same number.
This method gives us only the possible rational zeros. All of these might not be rational zeros of the polynomial and also there might be non-rational / complex zeros apart from these.
The numbers that we obtain from the Rational Root Test are possible zeros, it is not necessary that all of them are zeros of the polynomial.
All polynomials in one variable of degree n, n > 0, has at least one real or complex zero. This is the Fundamental Theorem of Algebra.To find all the possible rational zeros of a polynomial we use the Rational Root Test. Understanding Properties of Rational Exponents is always challenging for me but thanks to all math help websites to help me out.
Problems on Rational Root Test:
If a polynomial function has integer coefficients, then all the rational zeros will be of the form p/q where p is a factor of the constant and q is a factor of the leading coefficient.
Lets look at a few examples.
Ex 1: Find all the possible rational zeros of 2`x^(2)` + 6x +4
Here p = 4 and q = 2
The factors of 4 are 4,2 and 1
similarly the factors of 2 are 2 and 1
So all the possible rational zeros will be of the form : `( +-4, +-2, +-1)/( +-2, +-1)`
Now let us list out all the possible rational zeros: 4, 2, -4, -2, 1, -1, `(1)/(2)` , `(-1)/(2)` .
Ex 2: Find all the possible rational zeros of 2`x^(4)` - 7`x^(3)` +3x + 6.
Here p = 6. The factors of 6 are 3, 2, 1
q = 2. The factors of 2 are 2,1
So all the possible rational zeros will be of the form :`( +-3, +-2, +-1)/( +-2, +-1)`
Therefore the possible rational zeros are :
` ( 3)/(2)` , `(-3)/(2)` , 3, -3, 2, -2, 1, -1, `(1)/(2)` , `(-1)/(2)`
Is this topic how to calculate p value hard for you? Watch out for my coming posts.
Things that we should be Careful while Applying the Rational Root Test:
Always make sure the polynomial has integer coefficients. We have to multiply to get rid of fractions or decimals and later divide by the same number.
This method gives us only the possible rational zeros. All of these might not be rational zeros of the polynomial and also there might be non-rational / complex zeros apart from these.
The numbers that we obtain from the Rational Root Test are possible zeros, it is not necessary that all of them are zeros of the polynomial.
