Question

Find the relationship between zeros and x-intercepts of a2 + 5a + 6.

Answer 1

The x-intercepts, or zeros, which are the values of x(or a in this problem) for which the function is 0, are x = a = -2 and x = a = -3.

Explanation:

Suppose we have a function y = f(x). The zeros, which are the values of x for which y = 0, are also called the x-intercepts of the function.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

`ax^(2) + bx + c, a\\eq0`.

This polynomial has roots
`x_(1), x_(2)` such that
`ax^(2) + bx + c = a(x - x_(1))*(x - x_(2))`, given by the following formulas:

`x_(1) = (-b + √(\bigtriangleup))/(2*a)`

`x_(2) = (-b - √(\bigtriangleup))/(2*a)`

`\bigtriangleup = b^(2) - 4ac`

In this question:

I will write the function as a function of x, just exchanging a for x.

`f(x) = x^(2) + 5x + 6`

`\bigtriangleup = 5^(2) - 4*1*6 = 1`

`x_(1) = (-5 + √(1))/(2*1) = -2`

`x_(2) = (-5 - √(1))/(2*1) = -3`

The x-intercepts, or zeros, which are the values of x(or a in this problem) for which the function is 0, are x = a = -2 and x = a = -3.