HELP plz asap

[puppylover123]

Let p and q be real numbers such that the roots of x^2+px+q=0 are real. Prove that the roots of x^2+px+q+(x+a)(2x+p)=0 are real, for any real number a.

 

[Cubist]

Can you write the discriminant of both quadratics?

What do you know about the discriminant of the first quadratic?

 

[topsquark]

Let p and q be real numbers such that the roots of x^2+px+q=0 are real. Prove that the roots of x^2+px+q+(x+a)(2x+p)=0 are real, for any real number a.

This one seems to be going around on various forums.

Is there some reason you didn't reply to me here?

-Dan