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Solve using the quadratic formula. $\newline$ $5n^2 + 9n + 1 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $n =$ _ or $n =$ _

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Solve a quadratic equation using the quadratic formula

Full solution

Q. Solve using the quadratic formula.

\newline

5n^2 + 9n + 1 = 0

\newline

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

\newline

n =

_____ or

n =

_____

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic equation $5n^2 + 9n + 1 = 0$ . $a = 5$ , $b = 9$ , $c = 1$
Write quadratic formula: Write down the quadratic formula: $n = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ .
Substitute values: Substitute the values of $a$ , $b$ , and $c$ into the quadratic formula. $\newline$ $n = \frac{-\left(9\right) \pm \sqrt{\left(9\right)^2 - 4\left(5\right)\left(1\right)}}{2\left(5\right)}$
Calculate discriminant: Calculate the discriminant $(b^2 - 4ac)$ . $\newline$ Discriminant = $(9)^2 - 4(5)(1) = 81 - 20 = 61$
Insert into formula: Insert the discriminant into the quadratic formula. $\newline$ $n = \frac{-9 \pm \sqrt{61}}{2(5)}$ $\newline$ $n = \frac{-9 \pm \sqrt{61}}{10}$
Calculate solutions: Calculate the two possible solutions for $n$ . $n = \frac{{-9 + \sqrt{61}}}{{10}}$ or $n = \frac{{-9 - \sqrt{61}}}{{10}}$
Round to nearest hundredth: Round the values of $n$ to the nearest hundredth, if necessary. $n \approx (-9 + 7.81) / 10$ or $n \approx (-9 - 7.81) / 10$ $n \approx -1.19 / 10$ or $n \approx -16.81 / 10$ $n \approx -0.12$ or $n \approx -1.68$

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Question

h

is defined over the real numbers. This table gives a few values of

h

\newline

\begin{tabular}{lllll}

\newline

x

-6

1

-6

01

-6

001

-5

9

\newline

h(x)

-0

25

-0

74

-0

98

-1

0

\newline

\newline

What is a reasonable estimate for

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\newline

1

\newline

-6

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-2

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-1

\newline

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