Finding All Real Zeros Of A Polynomial With Examples (Second Example)Presentation Transcript
Finding all real zeros of a Polynomial Another example….
Find all the real zeros of Use the Rational Zeros Theorem to make a list of possible rational zeros
Find all the real zeros of Use your graphing calculator to narrow down the possible rational zeros the function seems to cross the x axis at these points….. we’ll use the remainder/factor theorem to be sure….
Find all the real zeros of Use the remainder and factor theorems to test the possible zeros since the remainder is zero, (x – 3/2) is a factor! since the remainder is not zero, (x + 3/2) is not a factor
Find all the real zeros of Use the divisor to divide the dividend 3/2 2 -3 -4 6 2 0 -4 0 3 0 -6 So the dividend is equal to:
Find all the real zeros of Synthetic division has allowed us to begin factoring the polynomial, now we can use other factor techniques to take care of the rest! Factor out the GCF And then use difference of two squares method to factor one last time
Find all the real zeros of Now that you have the polynomial in factored form, find those zeros!!! discard the constant Zeros: SOLUTION!!! So the zeros of f are the rational number +3/2 and the irrational numbers are and
Re-Cap of the Process
Use Rational Zeros Theorem to locate possible zeros
Use Calculator to narrow down possible zeros
Use Synthetic Division to rewrite the function as (divisor)(quotient)
Use the Zero Product Property to find all real zeros