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?

$p(x^2 + 9) + 5qx = 0 \Rightarrow px^2 + 5qx + 9p = 0$
$x= \frac{-5q \pm \sqrt{5^2q^2 -4\cdot9p^2}}{2p}$
Then you want the discriminant equal to 0. This is:
$5^2q^2 -4\cdot9p^2 = 0 \Rightarrow 5^2q^2 = 4\cdot9p^2 \Rightarrow 5q = 6p \Rightarrow p=\frac{5q}{6} \Rightarrow \frac{p}{q} = \frac{5}{6}$
Now the roots of the equation are:
$x= \frac{-5q}{2p} = \frac{-5\cdot6}{2\cdot5} = -3$
