Question 1 of 10:

What are the zeros of [tex][tex]$f(x)=x^2+x-20$[/tex][/tex]?

A. [tex][tex]$x=-4$[/tex][/tex] and [tex][tex]$x=5$[/tex][/tex]
B. [tex][tex]$x=-10$[/tex][/tex] and [tex][tex]$x=2$[/tex][/tex]
C. [tex][tex]$x=-2$[/tex][/tex] and [tex][tex]$x=10$[/tex][/tex]
D. [tex][tex]$x=-5$[/tex][/tex] and [tex][tex]$x=4$[/tex][/tex]



Answer :

To find the zeros of the quadratic function [tex]\( f(x) = x^2 + x - 20 \)[/tex], we need to solve the equation [tex]\( x^2 + x - 20 = 0 \)[/tex].

Let's solve this step-by-step by factoring the quadratic equation:

1. Write the equation: [tex]\( x^2 + x - 20 = 0 \)[/tex].

2. We need to find two numbers that multiply to give [tex]\(-20\)[/tex] (the constant term) and add to give [tex]\(1\)[/tex] (the coefficient of [tex]\(x\)[/tex]).

3. The two numbers that satisfy these conditions are [tex]\(5\)[/tex] and [tex]\(-4\)[/tex] because:
- [tex]\( 5 \times (-4) = -20 \)[/tex]
- [tex]\( 5 + (-4) = 1 \)[/tex]

4. Using these numbers, we can express the quadratic equation as:
[tex]\[ x^2 + x - 20 = (x + 5)(x - 4) = 0 \][/tex]

5. To find the zeros, we set each factor equal to zero:
[tex]\[ x + 5 = 0 \quad \text{or} \quad x - 4 = 0 \][/tex]
Solving these equations gives:
[tex]\[ x = -5 \quad \text{or} \quad x = 4 \][/tex]

So, the zeros of the function [tex]\( f(x) = x^2 + x - 20 \)[/tex] are [tex]\( x = -5 \)[/tex] and [tex]\( x = 4 \)[/tex].

Among the given choices, the correct answer is:
D. [tex]\( x = -5 \)[/tex] and [tex]\( x = 4 \)[/tex]