Question

Which equation is best to use to determine the zeros of the graph of y = 4x^2 – 8x - 5?

A.(2x + 1)(2x - 5) = 0

B.(2x - 1)(2x - 5) = 0

C.(4x - 1)(x - 5) = 0

D.(4x + 1)(x - 5) = 0 ​​

please answer ​

Answer 1

Using the Factor Theorem, it is found that the equation that is best used to determine the zeros of the graph of y = 4x^2 – 8x - 5 is:

A. (2x + 1)(2x - 5) = 0

What is the Factor Theorem?

The Factor Theorem states that a polynomial function with roots $x_1, x_2, \codts, x_n$ is given by:

$f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)$

In which a is the leading coefficient.

In this problem, the function is:

y = 4x² - 8x - 5.

Which is a quadratic function with coefficients a = 4, b = -8, c = -5, hence the solutions are found as follows.

$\Delta = (-8)^2 - 4(4)(-5) = 144$

$x_1 = \frac{8 + \sqrt{144}}{8} = \frac{5}{2}$

$x_2 = \frac{8 - \sqrt{144}}{4} = -\frac{1}{2}$

Hence, applying the Factor Theorem:

$y = \left(x - \frac{5}{2}\right)\left(x + \frac{1}{2}\right)$

Multiplying by 2:

y = (2x - 5)(2x + 1).

Hence option A is correct.

More can be learned about the Factor Theorem at https://brainly.com/question/24380382