Question

What are the zeros of the quadratic function f(x) = 2x² - 10x - 3?

A) x = 1, x = -3
B) x = 3, x = -1
C) x = 1, x = 3
D) x = -1, x = -3

Answer 1

The zeros of the quadratic function provided cannot be directly matched to the options given by the student, as the solutions involve a square root that does not produce neat integers. The student might have a typo in either the options or the equation itself.

Step-by-step explanation:

The zeros of the quadratic function f(x) = 2x² - 10x - 3 can be found by using the quadratic formula. For any quadratic equation of the form ax²+bx+c = 0, the solution for x can be calculated using:

x = [-b ± sqrt(b²-4ac)]/(2a)

In our function, a=2, b=-10, and c=-3. Plugging these values into the formula gives us:

x = [10 ± sqrt((-10)²-4(2)(-3))]/(2*2)

Simplifying further:

x = [10 ± sqrt(100+24)]/4 = [10 ± sqrt(124)]/4

Since sqrt(124) is not a perfect square, we can see that the given options in the student's question are incorrect because they include only integers. This hints at a possible mistake in either the given function or the options presented. Therefore, without correctly identified options, we cannot match our solution to one of the provided choices.