Question

Find the zeros of the function f(x) = 2x² + 20x + 46. Round values to the

nearest hundredth (if necessary).

Answer 1

-6.50

Explanation:

The zeros of the function are the x-values that make f(x) equal to zero. To find the zeros of this quadratic function, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Where a = 2, b = 20, and c = 46. Plugging in the values:

x = (-20 ± √(20² - 4 * 2 * 46)) / 2 * 2

x = (-20 ± √(400 - 184)) / 4

x = (-20 ± √216) / 4

x = (-20 ± √6 * √6) / 4

x = (-20 ± 6) / 4

So the zeros are x = (-20 + 6) / 4 = (-14) / 4 = -3.5 and x = (-20 - 6) / 4 = -26 / 4 = -6.5.

Rounding to the nearest hundredth, the zeros are approximately -3.50 and -6.50.