Real Roots and Imaginary Roots

May 15th, Friday, in a classroom at Nangang Second High School, Grade 12, Class 2.

After the last class of the morning ended, Chen Xiaoting quietly said to Shen Qi, "Shen Qi, want to go see a movie this Sunday?"

Shen Qi shook his head, "A movie this Sunday? I'm busy. You really know how to pick a time, you're doing it on purpose!"

Chen Xiaoting looked around furtively, then chided, "Hey, can you keep your voice down?"

Shen Qi lowered his voice slightly, "I'm really busy this Sunday. I'm going to participate in the Provincial High School Mathematics League. I've already registered."

"Oh, I see. Then the Math League is definitely the priority. Next time, another day." Chen Xiaoting breathed a sigh of relief, but also felt a little regretful. "But I only have half a day free this Sunday. I don't know when I'll have free time again. Shen Qi, I'm really grateful that you tutor me in math every day. I've improved a lot in solving math problems now. I sincerely want to treat you to a movie, or dinner, or something, to show my gratitude."

"We're classmates, and you're my deskmate. Don't say such corny things, it hurts our friendship."

"Okay, I'm being vulgar. I wish you victory and a triumphant return from the Math League!"

"Chen Xiaoting, what did you just say? Treat me to a meal? Then treat me to a simple meal."

"..."

Shen Qi and Chen Xiaoting arrived at a chain Chinese restaurant outside the school. It was busy during lunchtime, crowded with people, mostly students from nearby.

Nangang Second High School certainly had a cafeteria, but the cafeteria's mass-produced food was unappetizing. Students either ate at home or found food outside school.

Shen Qi and Chen Xiaoting lined up to order. Chen Xiaoting voluntarily stood in front of Shen Qi; she was treating them to lunch.

"Shen Qi, there are three set meals: Spicy Chicken Leg Rice + Overlord Flower Dragon Bone Soup, Potato Beef Brisket Rice + American Ginseng Black Chicken Soup, and Salted Fish Eggplant Rice + American Ginseng Black Chicken Soup. Which one do you want? I can order on my phone, and we can pay together on the phone to save five yuan." Chen Xiaoting operated her phone and asked.

"Don't rush to order yet. There's a bug here." Shen Qi had been staring at the restaurant's order information screen.

Chen Xiaoting was confused, "Bug?"

The line continued to move, and Chen Xiaoting reached the ordering counter.

"Welcome, pretty lady. What would you like to order?" the young male staff member asked enthusiastically.

Chen Xiaoting turned to ask Shen Qi, "I'll have the Potato Beef Brisket Rice + American Ginseng Black Chicken Soup set meal. How about you?"

Shen Qi stepped forward to the counter and said, "Your Spicy Chicken Leg Rice + Overlord Flower Dragon Bone Soup set meal is 30 yuan, the Potato Beef Brisket Rice + American Ginseng Black Chicken Soup set meal is 28 yuan, and the Salted Fish Eggplant Rice + American Ginseng Black Chicken Soup is 25 yuan. These are actually combinations of three main dishes and two soups."

The young staff member smiled, "That's right. This student is really good at math. You and this pretty lady are together, right? Which set meal would you like? There's a discount for mobile payment."

Shen Qi spoke unhurriedly, "Your menu information shows that the Spicy Chicken Leg Rice is sold separately for 22 yuan, and the Potato Beef Brisket Rice and Salted Fish Eggplant Rice are priced at 20 yuan and 15 yuan respectively."

The young staff member maintained his professional smile but was starting to get impatient, "Are you buying the main dish separately without the soup?"

"No, my classmate and I are here to eat, and we mainly want to drink the soup. Your soups are good."

"Then which set meal would you like?"

"Before ordering, I need to clarify one issue, which is the individual price of the two soups. Although you haven't published the prices of the soups, I can deduce the prices of the Overlord Flower Dragon Bone Soup and the American Ginseng Black Chicken Soup using a simple system of equations." Shen Qi looked at the menu screen again, having already calculated the result.

"..." The young staff member stopped smiling, thinking, What's wrong with this guy?

Chen Xiaoting was bewildered. Shen Qi, I'm treating you to lunch, don't cause trouble!

Shen Qi said seriously, "Here, let the price of the Overlord Flower Dragon Bone Soup be x, and let the price of the American Ginseng Black Chicken Soup be y. This gives us three linear equations, combined into a system of linear equations."

"Through not complicated calculations, I obtained a value for x, which means the price of the Overlord Flower Dragon Bone Soup is 8 yuan. OK, that's not a problem."

"But it's worth noting that there are two possible values for y, which are 8 and 10."

"This means your American Ginseng Black Chicken Soup can be sold for 8 yuan a bowl or 10 yuan a bowl. In a system of linear equations, the same y cannot have two real roots. This leads to another problem: does the price of your American Ginseng Black Chicken Soup have imaginary roots? What is the truth? Please tell me. As a consumer, I have the right to know the truth."

"I... I..." The young staff member was speechless. He cursed inwardly, What the hell should I tell you! If I could solve for imaginary roots, would I be smiling and selling fast food here?

"Holy crap, a scholar!"

"Spotted a wild scholar!"

"Which school are you from, classmate? Second High or Seventh High? Let's be friends, maybe even a couple! Should I add you or you add me?"

Many students were queuing to buy food, and Shen Qi was instantly surrounded.

"Pfft~" Chen Xiaoting, who had looked confused moments ago, chuckled. Shen Qi's explanation seemed to make sense. Why could the same soup have two different prices? What was the truth? Shen Qi's observational skills were quite sharp. Most normal people wouldn't pay attention to such details, but Shen Qi did.

"Yeah, why does the price of your soup have two real roots?"

"This is unscientific!"

"Shady establishment?"

"We need a reasonable explanation!"

"Hey, 12315 Consumer Protection Association? There's a shady establishment at number 233 Tianhe East Street 8, I want to report them!"

"Should I call 110 for reporting? Then please transfer me to 110."

The surrounding students who were just watching the commotion joined in, and the ordering counter became chaotic.

"Classmates, please calm down!"

"Be rational! Be sensible!"

"Stop fooling around, classmates. You're all educated people!"

The male and female staff members were in a panic. No one could answer Shen Qi's math problem. All they could do was try to appease these rowdy teenagers.

In this critical moment, the store manager stepped forward. "Our store does not have imaginary roots, and each soup has only one real root price! There was a display error, and the set meal price information was displayed incorrectly!" After all, the store manager was more educated.

"Manager, what I actually want is an explanation of an Abelian group, do you understand?" Shen Qi enjoyed talking with professionals.

To hell with your Abelian group, I don't understand, are all high school students these days so punchable? The manager couldn't answer Shen Qi's question, but he had already discovered the root of the confusion. It was actually the 2-dollar difference in their American Ginseng Black Chicken Soup. In short, they had been caught out, and it was annoying to think about. If the Administration for Industry and Commerce didn't care, why was this high school student fussing about it?

"The unit price for all our stew pots has only one real root, which is 8 yuan! The price information for the Salted Fish Eggplant Rice + American Ginseng Black Chicken Soup is displayed incorrectly. It's not 25 yuan, but 23 yuan! Customers who have already purchased this set meal can get a 2-yuan refund with their receipt!" The manager reacted quickly and immediately implemented emergency measures.

"If you explain it like that, it's barely reasonable." Shen Qi nodded, then said to Chen Xiaoting, "Let's both order the Salted Fish Eggplant Rice + American Ginseng Black Chicken Soup set. Considering the correction value and discount value, we can save a total of 9 yuan, which is an 8.2% discount. It's not good for a girl to treat me, a man, to a meal, so I'll save you a little if I can."

"Okay, to save a few yuan, you're bringing up real and imaginary roots. Shen Qi, you're really trying hard!" Chen Xiaoting scanned the QR code with her phone and bought two Salted Fish Eggplant Rice set meals.