(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that for all real values of a and b , the roots of the eqn : ax^2-(2a+b)x+b-5a=0

are real and different roots

2. Relevant equations

discriminat=b^2-4ac

where a is the x^2 coefficient and b is the x coefficient and c is the absolute term

3. The attempt at a solution

(2a+b)^2 - (4a(b-5a)) = 4a^2+b^2+4ab - 4ab+20a^2 = 4a^2+b^2+20a^2

so in order to solve the problem 4a^2+b^2+20a^2 should be > zero

and of course 4a^2+b^2+20a^2 >=0

but if a and b are zero then whole expression is gonna be zero thus the roots are real but the same

so can u help me??

Thanks

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# Homework Help: What is the discriminant for this quadratic?

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