Concept explainers
To find: rational zeros of function using rational zero test.
Answer to Problem 53CR
Explanation of Solution
Given information:
Concept used: - Rational root test:- Let f(x) be a polynomial and c be constant term in f(x) and a is leading coefficient of f(x) then ratio of possible divisors of constant term and leading coefficient can rational zeros of function.
Rational root =
1stmethod:-
Since, we know zeros of a polynomial satisfies polynomial so, by putting these numbers in polynomial we can check which number is zero of polynomial.
2ndmethod: - using synthetic division method we can also check the roots of polynomial.
Calculation: applying rational root test for h(x), we have
Possible divisors of constant term c = 6 are
And possible divisors of leading coefficient term is 1
Since, h(x) is 2 degree polynomial so it has 2 zeros -2, -3
(As we have found 2 zeros for 2 degree polynomial so no need to test further for zeros).
Zeros of g(x) = 0, 0
As
Therefore, zeros of f(x) is 0, 0, -2, -3.
Chapter 2 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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