Question

Thomas creates the table shown to represent the function f(x) = x + 3x - 10.

Answer 1

The zeros of the equation are A)  x = -5 and x = 2

Step-by-step explanation:

The equation given is

$f(x)=x^2+3x-10$

Which is a second-order equation written in the form

$f(x)=ax^2+bx+c$

where here:

a = 1

b = +3

c = -10

The solutions (the zeros) of an equation wirtten in this form can be found by using the following:

$x_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Substituting the values of a, b and c for this equation, we find:

$x_{1,2}=\frac{-3\pm \sqrt{(3)^2-4(1)(-10)}}{2(1)}=\frac{-3\pm \sqrt{9+40}}{2}=\frac{-3\pm 7}{2}$

Which gives two values:

x = -5

x = 2

Therefore, these values are the zeros of the equation, so the correct option is

A)  x = -5 and x = 2

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