## Algebra 1: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 10 - Radical Expressions and Equations - Get Ready! - Page 611: 17

#### Answer

No 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, $x^2-2x+9=0$, $a=1$, $b=-2$ and $c=9$. $D= b^2-4ac= (-2)^2-4*1*9=4-36=-32<0$ Therefore, this equation has no real solutions.

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