There is no such value of 'a' such that f(x) = 9x² + 4 and g(x) = (3x - a)² are equivalent.
<h3>What are equivalent polynomials?</h3>
Two polynomials are said to be equivalent only when the coefficients of all powers of x are equal for both the polynomials.
<h3>How to solve the question?</h3>
In the question, we are asked is there a value of 'a' such that f(x) = 9x² + 4 and g(x) = (3x - a)² are equivalent.
We know that two polynomials are said to be equivalent only when the coefficients of all powers of x are equal for both the polynomials.
Thus to check, we expand g(x), using the formula (p - q)² = p² + q² - 2pq.
g(x) = (3x - a)²,
or, g(x) = (3x)² + (a)² - 2(3x)(a),
or, g(x) = 9x² + a² - 6ax.
For f(x) = 9x² - 4, and g(x) = (3x - a)² to be equivalent,
- -6ax should be 0, that is, a should be 0,
- a² should be 4, that is, a needs to be 2, or -2.
As we need two different values of, 'a' at the same time, which ain't possible, thus we can say that there is no such value of 'a' such that f(x) = 9x² + 4 and g(x) = (3x - a)² are equivalent.
Learn more about equivalent polynomials at
brainly.com/question/10191748
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