Prove that this equation has two rational roots if a does not = c
ago in Algebra 1 Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

Best answer

a(x^2 +x) + c(x+1)=0

=> ax^2 + ax + cx +c =0

=> ax^2 + (a+c)x +c = 0

So discriminant D = (a+c)^2 - 4ac

=> D = a^2 + 2ac + c^2 -4ac

=> D= a^2 - 2ac + c^2

=> D = (a-c)^2

The square confirms that the roots are real and rational. Since (a-c)^2 is always greater than or equal to zero and is always a perfect square(making it rational).

But if a = c then,

D = (a-c)^2 = (a-a)^2 = 0

And we know when D=0 it has one and only one real root.

Therefore, to satisfy the condition D>0 ie having 2 real roots a must not equal to c.

 

 

 

 

ago by Level 5 User (12.5k points)

Related questions

0 answers
0 answers
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
85,401 questions
90,910 answers
2,183 comments
103,217 users