Question
(A) Use the quadratic formula to solve this equation and find the appropriate integer values of \( N, M \), and \( D \). Do not worry about simplifying the \( \sqrt{D} \) yet in this part of the problem. \[ N=13 ; D=361 \] (B) Now simplify the radical and the resulting solutions. Enter your answers as a list of integers or reduced fractions, separated with commas. Example: \( -5 / 2,-3 / 4 \) \[ t=\square \]
Ask by Morgan Ellis. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( t = \frac{19}{13}, -\frac{19}{13} \)
Solution
### Part (B)
Given that \( N = 13 \) and \( D = 361 \), we can simplify the solutions using the quadratic formula:
\[
t = \frac{-M \pm \sqrt{D}}{N} = \frac{-M \pm \sqrt{361}}{13} = \frac{-M \pm 19}{13}
\]
Assuming \( M = 0 \) (since no specific value for \( M \) was provided), the solutions simplify to:
\[
t = \frac{19}{13}, \frac{-19}{13}
\]
**Answer:** \( t = 19/13,-19/13 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To solve the quadratic equation \( Ax^2 + Bx + C = 0 \) using the quadratic formula \( x = \frac{-B \pm \sqrt{D}}{2A} \), we can plug in the values \( N=13 \) and \( D=361 \). With \( A=1, B=-13, \) and \( C=0 \) (since the equation simplifies to \( x^2 - 13x = 0 \)), we first calculate \( x = \frac{13 \pm \sqrt{361}}{2} \). Now, simplifying further, we know that \( \sqrt{361} = 19 \). Thus, the solutions become \( x = \frac{13 + 19}{2} \) and \( x = \frac{13 - 19}{2} \), leading to the integer solutions \( x = 16 \) and \( x = -3 \). So the integers are: \[ t = 16, -3 \]
