A quadratic equation z² + aiz+ag=0 with real coefficients a, and of will always have two solutions, but those solutions might not be real and they might be repeated. For example, the equation z²+02-1=0 can be solved by selecting z=1 or z=-1, meaning that it has two real solutions; however, the equation z2 +0z+1=0 cannot be solved using real numbers, while the equation r²-2r+1=0 has z=1 as both of its solutions. Write a definition for a new predicate, AllPositive(a,, ag), which tells us that all real solu- tions to the equation 2+ar+ao = 0 must be positive numbers.
A quadratic equation z² + aiz+ag=0 with real coefficients a, and of will always have two solutions, but those solutions might not be real and they might be repeated. For example, the equation z²+02-1=0 can be solved by selecting z=1 or z=-1, meaning that it has two real solutions; however, the equation z2 +0z+1=0 cannot be solved using real numbers, while the equation r²-2r+1=0 has z=1 as both of its solutions. Write a definition for a new predicate, AllPositive(a,, ag), which tells us that all real solu- tions to the equation 2+ar+ao = 0 must be positive numbers.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.6: Solving Quadratic Equations By Using The Quadratic Formula
Problem 57HP
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Question
![A quadratic equation z² + aiz+ao=0 with real coefficients a, and as will always
have two solutions, but those solutions might not be real and they might be repeated. For
example, the equation z²+02-1=0 can be solved by selecting z = 1 or z=-1, meaning
that it has two real solutions; however, the equation z²+0z+1=0 cannot be solved using
real numbers, while the equation r2-2x+1=0 has r= 1 as both of its solutions.
Write a definition for a new predicate, AllPositive(a,, ag), which tells us that all real solu-
tions to the equation z2+ ajr+ ao=0 must be positive numbers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F032f9f2f-4a86-4f7c-abbd-a161821f35fd%2F1443201f-e333-44fc-b750-a4e4f0935971%2Fm385j3h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A quadratic equation z² + aiz+ao=0 with real coefficients a, and as will always
have two solutions, but those solutions might not be real and they might be repeated. For
example, the equation z²+02-1=0 can be solved by selecting z = 1 or z=-1, meaning
that it has two real solutions; however, the equation z²+0z+1=0 cannot be solved using
real numbers, while the equation r2-2x+1=0 has r= 1 as both of its solutions.
Write a definition for a new predicate, AllPositive(a,, ag), which tells us that all real solu-
tions to the equation z2+ ajr+ ao=0 must be positive numbers.
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