text: ## Precalculus (6th Edition)
  
  Francesca was wrong because the quadratic formula works even when $b=0$.
  RECALL: The quadratic equation $ax^2+bx+c=0$ can be solved using the quadratic formula: $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ The given equation has: $a=1, b=0, c=-19$ Substitute these values into the quadratic formula to obtain: $x=\dfrac{-0 \pm \sqrt{0^2-4(1)(-19)}}{2(1)} \\x=\dfrac{\pm\sqrt{0+76}}{2} \\x=\dfrac{\pm\sqrt{76}}{2} \\x=\dfrac{\pm\sqrt{4(19)}}{2} \\x=\dfrac{2\sqrt{19}}{2} \\x=\pm\sqrt{19}$ Thus, the solution set is $\color{blue}{\left\{-\sqrt{19}, \sqrt{19}\right\}}$. Francesca was wrong because the quadratic formula actually works regardless of whether $b=0$ or not.
explanation: The document provides a detailed explanation and solution to a quadratic equation problem. It includes a statement that Francesca was wrong about the quadratic formula not working when \( b = 0 \), and then proceeds to solve the equation \( x^2 - 19 = 0 \) using the quadratic formula. The solution set is given as \( \left\{-\sqrt{19}, \sqrt{19}\right\} \).
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: ## Precalculus (6th Edition)
  
  Francesca was wrong because the quadratic formula works even when $b=0$.
  RECALL: The quadratic equation $ax^2+bx+c=0$ can be solved using the quadratic formula: $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ The given equation has: $a=1, b=0, c=-19$ Substitute these values into the quadratic formula to obtain: $x=\dfrac{-0 \pm \sqrt{0^2-4(1)(-19)}}{2(1)} \\x=\dfrac{\pm\sqrt{0+76}}{2} \\x=\dfrac{\pm\sqrt{76}}{2} \\x=\dfrac{\pm\sqrt{4(19)}}{2} \\x=\dfrac{2\sqrt{19}}{2} \\x=\pm\sqrt{19}$ Thus, the solution set is $\color{blue}{\left\{-\sqrt{19}, \sqrt{19}\right\}}$. Francesca was wrong because the quadratic formula actually works regardless of whether $b=0$ or not.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document provides a detailed explanation and solution to a quadratic equation problem. It includes a statement that Francesca was wrong about the quadratic formula not working when \( b = 0 \), and then proceeds to solve the equation \( x^2 - 19 = 0 \) using the quadratic formula. The solution set is given as \( \left\{-\sqrt{19}, \sqrt{19}\right\} \).
  
  Label: question-and-answer