Question

Given the quadratic function f(x) = 4x² +7x+c, where c is some real number constant. If c = 3, are thezeroes of f(x) rational or irrational numbers? Explain how you arrived at your choice.

Answer 1

The zeros are rational numbers

Step-by-step explanation:

When we have an equation of the form

f(x) = ax² + bx + c

The zeros of the function are rational if b² - 4ac ≥ 0 and irrational if b² - 4ac < 0

In this case, we have the equation

f(x) = 4x² + 7x + c

Where c = 3, so the equation is

f(x) = 4x² + 7x + 3

Now, a = 4, b = 7, and c = 3, so the term b² - 4ac is equal to:

b² - 4ac = 7² - 4(4)(3)

b² - 4ac = 49 - 48

b² - 4ac = 1

Since 1 is greater than 0, we can say that the zeros are rational numbers.