Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 10 - Radical Expressions and Equations - Get Ready! - Page 611: 15


2 real solutions.

Work Step by Step

To find the number of solutions in a quadratic formula, we need to find the determinant. The determinant follows these rules: If D<0: no real solutions If D=0: 1 real solution If D>0: 2 real solutions The determinant is generally calculated by this formula: $ D={b^2-4ac}$. The general formula for quadratic equations is: $ax^2+bx+c=0$ Therefore, in this equation, $x^2+6x+1=0$, $a=1$, $b=6$ and $c=1$. $D= b^2-4ac= 6^2-4*1*1=36-4=32>0$ Therefore, this equation has 2 real solutions.
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