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Which of the following is a zero of the function f(x)

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Which of the following is a zero of the function f(x) = 2x3 + 3x2 - 3x - 2.
A. -2
B. -1
C. 1212121
D. 2
c1/3

 

asked Sep 3, 2014 in ALGEBRA 2 by tonymate Pupil
edited Sep 3, 2014 by tonymate

1 Answer

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Best answer

Identify Rational Zeros :

Usually it is not practical to test all possible zeros of a polynomial function using only synthetic substitution. The Rational Zero Theorem can be used for finding the some possible zeros to test.

Rational Root Theorem, if a rational number in simplest form p/q is a root of the polynomial equation anx n + an  1x n – 1 + ... + a1x + a0 = 0, then p is a factor of a0 and q is a factor if an.

The function is 2x 3 + 3x 2- 3x - 2 = 0.

If p/q is a rational zero, then p is a factor of - 2 and q is a factor of 2.

The possible values of p are   ± 1 and ± 2.

The possible values for q are ± 1 and ± 2.

By the Rational Roots Theorem, the only possible rational roots are, p / q = ± 1, ± 2 and ± 1/2.

Make a table for the synthetic division and test possible real zeros.

p/q

2

3

- 3

- 2

1

2

5

2

0

Since, f(1) = 0, x = 1 is a zero. The depressed polynomial is 2x 2 + 5x + 2 = 0.

By factor by grouping.

2x 2 + 5x + 2 = 0

2x 2 + 4x + x + 2 = 0

2x(x + 2) + 1(x + 2) = 0

Factor : (2x + 1)(x + 2) = 0

Apply zero product property.

2x + 1 = 0 and x + 2 =  0

x = - 1/2 and x = - 2.

Therefore, tthe roots of the function are x = - 2, x = - 1/2, and x = 1.

The option A is correct.

answered Sep 3, 2014 by casacop Expert
selected Sep 3, 2014 by tonymate

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