Given the quadratic equation $p(x^2 +9)= -5qx$ has two equal roots, find the ratio of $p:q$. Hence, solve the quadratic equation Given the quadratic equation $p(x^2 +9)= -5qx$ has two equal roots, find the ratio of p:q. Hence, solve the quadratic equation
so this is what i got so far :
$$px^2+9p+5qx=0$$
$$(5q)^2 - 4(p)(9p)=0$$
$$25q^2 - 36p^2 =0$$
$$(5^2 q^2) - (6^2 p^2)=0$$
$$5^2 q^2 = 6^2 p^2$$
$$5q =6p$$
I might be wrong
what to do next?

Answer 1 -
When we have equal roots then discriminate equals to zero. As you are solving.
Answer 2 -
We have,
5q = 6p
$\frac{p}{q} = \frac56$
Or
You can also write
$(5^2 q^2) - (6^2 p^2) = 0$
As $(5q)^2 - (6p)^2 = 0$
$(5q - 6p)(5q + 6p) = 0$
Either 5q - 6p = 0 or 5q + 6p = 0
$\frac{p}{q} = \frac56$ or $\frac{p}{q} = \frac{-5}{6}$
Answer 3 -
For equal roots we have each root equals to $\frac{-b}{2a}$
So x = $\frac{-5q}{2p}$
=  $\frac{-5}{2} \times \frac{6}{5}$
x = -3
