Question

H(x) = x² - 7x - 81) What are the zeros of the function?

Write the smaller t first, and the larger t second.
smaller x=___
larger x= ____

Answer 1

The zeros of the function h(x) are found using the quadratic formula, resulting in approximately -6.16 for the smaller x and 13.16 for the larger x.

Step-by-step explanation:

To find the zeros of the function h(x) = x² - 7x - 81, we use the quadratic formula, which applies to equations of the form ax² + bx + c = 0. For the given function, a = 1, b = -7, and c = -81.

The quadratic formula is given by:

x = (-b ± √b² - 4ac) / (2a)

Plugging in the values from our function:

x = (7 ± √(7² - 4(1)(-81))) / (2(1))

x = (7 ± √(49 + 324)) / 2

x = (7 ± √373) / 2

Since √373 is approximately 19.3132, our two solutions are:

x = (7 + 19.3132) / 2 and x = (7 - 19.3132) / 2

x ≈ 13.1566 and x ≈ -6.1566

Therefore, the smaller x is approximately -6.16 and the larger x is approximately 13.16.