133k views
2 votes
Consider the cubic function y = f(x) = -4x^3 – 6x^2 + 3x + 7.

Use the Rational Zeroes Theorem to list the possible rational zeroes of f(x). ____________

1 Answer

3 votes

Answer:

The all possible rational zeroes of f(x) are
\pm 1,\pm (1)/(2),\pm (1)/(4),\pm7,\pm (7)/(2),\pm (7)/(4),

Explanation:

Consider the provided cubic function.


y = f(x) = -4x^3 -6x^2 + 3x + 7

Rational zeros Theorem states that:

If P(x) is a polynomial and if p/q is a zero of P(x), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x).

Therefore,

The factor of constant term: ±1, ±7

Factors of leading coefficient: ±1, ±2, ±4

The Possible values of p/q:
\pm (1,\:7)/(1,\:2,\:4)=\pm 1,\pm (1)/(2),\pm (1)/(4),\pm7,\pm (7)/(2),\pm (7)/(4),

Hence, the all possible rational zeroes of f(x) are
\pm (1,\:7)/(1,\:2,\:4)=\pm 1,\pm (1)/(2),\pm (1)/(4),\pm7,\pm (7)/(2),\pm (7)/(4),

Note: These are all possible rational zeroes.

The rational zeros of the provided cubic function is x=1.

Substitute x=1 in provided function.


-4\cdot \:1^3-6\cdot \:1^2+3\cdot \:1+7=0\\0=0

Which is true.

Hence, the rational zeros of the provided cubic function is x=1.

User Tadej
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories