Question

If the equation x +9x +p= 0 has real roots, then (a) ps (b) p <= (c)p 2 (d) p 2​

Answer 1

Answer:

ANSWER

Let α+iβ,α−iβ be the roots.

Then α

2

+β

2

=

p

r

>0.

So, p,r are of the same sign.

Also p+r>0.

So, p,r are both positive.

If q<0,p−q+r>0.

If q>0,(p+r)

2

−(p−r)

2

=4pr≥q

2

(∵ Roots are non-real).

∴(p+r)

2

≥q

2

+(p−r)

2

≥q

2

∴p+r>q.