Answer:
(b) 1/3
Explanation:
A function "zero" is a value of x that makes the value of the function be zero. It may also be called a "root" of the function. On a graph, it is an x-intercept.
The zeros are the solutions to the equation f(x) = 0. For a quadratic like the one given, there are two of them. For this function, they are distinct, so one will be larger than the other.
Graph
There are a number of ways the solutions to this equation can be found. Technology, in the form of a graphing calculator, can show you the x-intercepts easily (see attached). They are x=-2/5 and x=1/3.
Factoring
We can also factor the equation. Doing this requires that we find factors of the product (15)(-2) = -30 that have a sum equal to the coefficient of x, +1. Here are some factor pairs:
-30 = (-1)(30) = (-2)(15) = (-3)(10) = (-5)(6)
The corresponding sums are 29, 13, 7, 1. Hence the last factor pair, {-5, 6}, is the one we need.
Rewriting the 3-term polynomial to a 4-term polynomial by splitting the middle term using these factors, we have ...
15x² -5x +6x -2 = 0
Factoring pairs of terms gives ...
5x(3x -1) +2(3x -1) = 0
(5x +2)(3x -1) = 0 . . . . . . . factor out the common factor
The product of these factors can only be zero of one of them is zero. (This is the "zero product rule.") Setting the factors to zero, we find the values of x that make f(x) = 0: the zeros of the function.
5x +2 = 0 ⇒ x = -2/5
3x -1 = 0 ⇒ x = 1/3
The zeros of the function are -2/5 and 1/3.
The larger zero is 1/3.