Answer:
The relationship between d, c and p is that [tex]p = \frac{4c^2}{9d}[/tex]
Step-by-step explanation:
Roots of a quadratic equation:
The roots [tex]r_1[/tex] and [tex]r_2[/tex] of a quadratic equation in the following format:
[tex]ax^2 + bx + c = 0[/tex]
Can be given by:
[tex]r_1 + r_2 = -\frac{b}{a}[/tex]
[tex]r_1r_2 = \frac{c}{a}[/tex]
In this question:
We have the following quadratic equation:
[tex]dx^2 - cx + p = 0[/tex]
So [tex]a = d, b = -c, c = p[/tex]
One of the roots is twice the other:
So [tex]r_2 = 2r_1[/tex]
First relation:
[tex]r_1 + r_2 = -\frac{b}{a}[/tex]
[tex]r_1 + 2r_1 = -\frac{(-c)}{d}[/tex]
[tex]3r_1 = \frac{c}{d}[/tex]
[tex]r_1 = \frac{c}{3d}[/tex]
Second relation:
[tex]r_1r_2 = \frac{c}{a}[/tex]
[tex]r_1*2r_1 = \frac{p}{d}[/tex]
[tex]2r_{1}^{2} = \frac{p}{d}[/tex]
[tex](\frac{2c}{3d})^2 = \frac{p}{d}[/tex]
[tex]\frac{4c^2}{9d^2} = \frac{p}{d}[/tex]
[tex]p = \frac{4c^2}{9d}[/tex]
The relationship between d, c and p is that [tex]p = \frac{4c^2}{9d}[/tex]
