quadratic equation

Question

Let a,b and c be real number such that 4a+2b+c=0 and ab>0 then quadratic equation ax^2+bx+c=0 has 

A. real roots

B.complex roots

C. purely imaginary

D. only one root

Answer 1

     Doing what I did in your other problem, the discriminant is b^2 - 4ac. replacing c with -4a - 2b we get b^2 - 4a( -4a - 2b ). Simplifying we get b^2 + 16a^2 + 8ab. Squaring always results in a positive number so the first 2 terms of the expression are positive. Part of your initial conditions stated ab>0, therefore 8ab>0 or is positive. So your discriminant is always positive and therefore when you place it under the sqrt, you end up with sqrt of a positive which is always a real number.