Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 9 - Quadratic Functions and Equations - Cumulative Test Prep - Short Response - Page 596: 26

Answer

Sometimes true. Two equations are $10x^2+5x+1=0$ and $2x^2+4x+2=0$

Work Step by Step

One example of an equation without two solutions is $2x^2+4x+2=0$ The determinant is as follows: $b^2-4ac$ $4^2-4*2*2$ $16-8*2$ $16-16$ $0$ Since this determinant is zero, there is exactly one real solution for the equation. Another equation without two solutions is $10x^2+5x+1=0$ The determinant is as follows: $b^2-4ac$ $5^2-4*10*1$ $25-40$ $-15$ Since this determinant is less than zero, there are no real solutions for the equation.
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