Question

time taken by the express train = \frac{132}{x+11}

it is given that the express train took 1 hour less than the local train to reach 132 miles. i.e.,

\frac{132}{x} - \frac{132}{x+11} = 1

132 \left( \frac{1}{x} - \frac{1}{x+11} \
ight) = 1

132 \left( \frac{x+11-x}{x(x+11)} \
ight) = 1

132 \left( \frac{11}{x(x+11)} \
ight) = 1

\frac{1452}{x(x+11)} = 1

on simplifying it, x^2 + 11x - 1452 = 0

value: 3

match the items.
a. 1
b. 11
c. -1452

1. a
2. b
3. c

Explanation:

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<reasoning>

Identify the standard form of the quadratic equation

Using the Quadratic Equations knowledge point
\[

$$\begin{aligned} &ax^2 + bx + c = 0\\ &x^2 + 11x - 1452 = 0 \end{aligned}$$

\]

Match the coefficients to the given values

Using the Quadratic Equations knowledge point
\[

$$\begin{aligned} &a = 1\\ &b = 11\\ &c = -1452 \end{aligned}$$

\]

Map the matched coefficients to the items

Using the Quadratic Equations knowledge point
\[

$$\begin{aligned} &\text{Item a: } 1 \implies a \text{ (matches 1)}\\ &\text{Item b: } 11 \implies b \text{ (matches 2)}\\ &\text{Item c: } -1452 \implies c \text{ (matches 3)} \end{aligned}$$

\]
</reasoning>

<answer>

No.	Answer
2	b
3	c

</answer>

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Answer:

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<reasoning>

Identify the standard form of the quadratic equation

Using the Quadratic Equations knowledge point
\[

$$\begin{aligned} &ax^2 + bx + c = 0\\ &x^2 + 11x - 1452 = 0 \end{aligned}$$

\]

Match the coefficients to the given values

Using the Quadratic Equations knowledge point
\[

$$\begin{aligned} &a = 1\\ &b = 11\\ &c = -1452 \end{aligned}$$

\]

Map the matched coefficients to the items

Using the Quadratic Equations knowledge point
\[

$$\begin{aligned} &\text{Item a: } 1 \implies a \text{ (matches 1)}\\ &\text{Item b: } 11 \implies b \text{ (matches 2)}\\ &\text{Item c: } -1452 \implies c \text{ (matches 3)} \end{aligned}$$

\]
</reasoning>

<answer>

No.	Answer
2	b
3	c

</answer>

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