Textbook Question
Use the method described in Exercises 83–86, if applicable, and properties ofabsolute value to solve each equation or inequality. (Hint: Exercises 99 and 100 canbe solved by inspection.) | 3x^2 - 14x | = 5
386
views
1. Equations & Inequalities
The Quadratic Formula
Struggling with College Algebra?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Determine the number and type of solutions of the given quadratic equation. Do not solve.
A
2 real solutions
B
1 real solution
C
2 imaginary solutions
Verified step by step guidance1
Identify the quadratic equation in the standard form: \( ax^2 + bx + c = 0 \). In this case, \( a = 1 \), \( b = 8 \), and \( c = 16 \).
Use the discriminant formula \( b^2 - 4ac \) to determine the nature of the solutions. The discriminant helps us understand how many and what type of solutions the quadratic equation has.
Calculate the discriminant: \( b^2 - 4ac = 8^2 - 4 \times 1 \times 16 \).
Interpret the discriminant: If \( b^2 - 4ac > 0 \), there are 2 distinct real solutions. If \( b^2 - 4ac = 0 \), there is exactly 1 real solution (a repeated root). If \( b^2 - 4ac < 0 \), there are 2 complex (imaginary) solutions.
Based on the calculated discriminant, determine the number and type of solutions for the quadratic equation \( x^2 + 8x + 16 = 0 \).
6:36mWatch next
Master Solving Quadratic Equations Using The Quadratic Formula with a bite sized video explanation from Patrick
Start learningRelated Videos
Related Practice
The Quadratic Formula practice set
Problem sets built by lead tutorsExpert video explanations