Question

value: 5

match the items.

a. 1 and -\frac{1}{2}
b. 8 and -10
c. -20 and 13
d. 8 and 3
e. -3 and -14

1. 3n^2 - 33n + 72 = 0
2. x^2 + 7x - 260 = 0
3. m^2 + 17m + 42 = 0
4. 8a^2 - 4a = 4
5. m^2 + 2m = 80

Explanation:

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<reasoning>

Solve Equation 1

Using the Quadratic Equations and Factoring Quadratic Trinomials knowledge points
\[

$$\begin{aligned} &3n^2 - 33n + 72 = 0 \\ &3(n^2 - 11n + 24) = 0 \\ &3(n - 8)(n - 3) = 0 \\ &n = 8 \quad \text{or} \quad n = 3 \end{aligned}$$

\]
This matches option d.

Solve Equation 2

Using the Quadratic Equations and Factoring Quadratic Trinomials knowledge points
\[

$$\begin{aligned} &x^2 + 7x - 260 = 0 \\ &(x + 20)(x - 13) = 0 \\ &x = -20 \quad \text{or} \quad x = 13 \end{aligned}$$

\]
This matches option c.

Solve Equation 3

Using the Quadratic Equations and Factoring Quadratic Trinomials knowledge points
\[

$$\begin{aligned} &m^2 + 17m + 42 = 0 \\ &(m + 3)(m + 14) = 0 \\ &m = -3 \quad \text{or} \quad m = -14 \end{aligned}$$

\]
This matches option e.

Solve Equation 4

Using the Quadratic Equations and Factoring Quadratic Trinomials knowledge points
\[

$$\begin{aligned} &8a^2 - 4a - 4 = 0 \\ &4(2a^2 - a - 1) = 0 \\ &4(2a + 1)(a - 1) = 0 \\ &a = -\frac{1}{2} \quad \text{or} \quad a = 1 \end{aligned}$$

\]
This matches option a.

Solve Equation 5

Using the Quadratic Equations and Factoring Quadratic Trinomials knowledge points
\[

$$\begin{aligned} &m^2 + 2m - 80 = 0 \\ &(m + 10)(m - 8) = 0 \\ &m = -10 \quad \text{or} \quad m = 8 \end{aligned}$$

\]
This matches option b.
</reasoning>

<answer>

No.	Problem	Answer
2	\(x^2 + 7x - 260 = 0\)	c. -20 and 13
3	\(m^2 + 17m + 42 = 0\)	e. -3 and -14
4	\(8a^2 - 4a = 4\)	a. 1 and -\(\frac{1}{2}\)
5	\(m^2 + 2m = 80\)	b. 8 and -10

</answer>

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Answer:

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<reasoning>

Solve Equation 1

Using the Quadratic Equations and Factoring Quadratic Trinomials knowledge points
\[

$$\begin{aligned} &3n^2 - 33n + 72 = 0 \\ &3(n^2 - 11n + 24) = 0 \\ &3(n - 8)(n - 3) = 0 \\ &n = 8 \quad \text{or} \quad n = 3 \end{aligned}$$

\]
This matches option d.

Solve Equation 2

Using the Quadratic Equations and Factoring Quadratic Trinomials knowledge points
\[

$$\begin{aligned} &x^2 + 7x - 260 = 0 \\ &(x + 20)(x - 13) = 0 \\ &x = -20 \quad \text{or} \quad x = 13 \end{aligned}$$

\]
This matches option c.

Solve Equation 3

Using the Quadratic Equations and Factoring Quadratic Trinomials knowledge points
\[

$$\begin{aligned} &m^2 + 17m + 42 = 0 \\ &(m + 3)(m + 14) = 0 \\ &m = -3 \quad \text{or} \quad m = -14 \end{aligned}$$

\]
This matches option e.

Solve Equation 4

Using the Quadratic Equations and Factoring Quadratic Trinomials knowledge points
\[

$$\begin{aligned} &8a^2 - 4a - 4 = 0 \\ &4(2a^2 - a - 1) = 0 \\ &4(2a + 1)(a - 1) = 0 \\ &a = -\frac{1}{2} \quad \text{or} \quad a = 1 \end{aligned}$$

\]
This matches option a.

Solve Equation 5

Using the Quadratic Equations and Factoring Quadratic Trinomials knowledge points
\[

$$\begin{aligned} &m^2 + 2m - 80 = 0 \\ &(m + 10)(m - 8) = 0 \\ &m = -10 \quad \text{or} \quad m = 8 \end{aligned}$$

\]
This matches option b.
</reasoning>

<answer>

No.	Problem	Answer
2	\(x^2 + 7x - 260 = 0\)	c. -20 and 13
3	\(m^2 + 17m + 42 = 0\)	e. -3 and -14
4	\(8a^2 - 4a = 4\)	a. 1 and -\(\frac{1}{2}\)
5	\(m^2 + 2m = 80\)	b. 8 and -10

</answer>

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