Question

Find the zeros of the function f(x) = x² + 10x + 19. Round values to the nearest hundredth

(if necessary).
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Answer 1

To find the zeros of the function f(x) = x² + 10x + 19, we can use the quadratic formula. The zeros are approximately x₁ ≈ 0.55 and x₂ ≈ -10.55.

Step-by-step explanation:

To find the zeros of the function f(x) = x² + 10x + 19, we need to solve the equation x² + 10x + 19 = 0. We can solve this equation by factoring, completing the square, or using the quadratic formula. Since the quadratic equation cannot be factored easily, let's use the quadratic formula. The quadratic formula states that for a quadratic equation of the form ax² + bx + c = 0, the zeros can be found using the formula:

x = (-b ± √(b² - 4ac)) / (2a)

In our case, a = 1, b = 10, and c = 19. Substituting these values into the quadratic formula, we get:

x = (-10 ± √(10² - 4(1)(19))) / (2(1))

Simplifying further, we have:

x = (-10 ± √(100 - 76)) / 2

x = (-10 ± √24) / 2

x = (-10 ± 2√6) / 2

Simplifying once more, we have:

x = -5 ± √6

Rounding to the nearest hundredth, the zeros of the function f(x) = x² + 10x + 19 are approximately:

x₁ ≈ -5 + √6 ≈ 0.55

x₂ ≈ -5 - √6 ≈ -10.55

Learn more about Finding zeros of a quadratic function