SOLUTION: Use the Rational Root Theorem to list all possible rational roots for each equation. Then find any actual roots.
27. x3 + 2x2 + 3x + 6 = 0
28. x4 – 7x2 + 12 = 0
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Question 177550: Use the Rational Root Theorem to list all possible rational roots for each equation. Then find any actual roots.
27. x3 + 2x2 + 3x + 6 = 0
28. x4 – 7x2 + 12 = 0
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
The Rational Roots (or Rational Zeroes) Test is a handy way of obtaining a list of useful first guesses when you are trying to find the zeroes (roots) of a polynomial. Given a polynomial with integer (that is, positive and negative "whole-number") coefficients, the possible (or potential) zeroes are found by listing the factors of the constant (last) term over the factors of the leading coefficient, thus forming a list of fractions. This listing gives you a list of potential rational (fractional) roots to test -- hence the name of the Test.
27. x3 + 2x2 + 3x + 6 = 0
:
the factors of 6 are 1,2,3,6,-1,-2,-3,-6. 1 is our leading coefficent so we have all factors of 6 as possible roots
:
x4 – 7x2 + 12 = 0
:
the factors of 12 are 1,2,3,4,6,12,-1,-2,-3,-4,-6,-12 and again our leading coefficient is 1 so all the factors of 12 are possible roots.
:
I will leave it to you to find the actual root(you know all the possibles just plug them into the equations to see if they make the equation true) If you get 0=0 you know you have a solution. If not then it isnt a solution.
example:
pr 27 lets try 1 as a solution 14=0 so 1 is NOT a solution.
:
just keep plugging them in
:
GOOD LUCK
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