Question 8

Explanation

Let the polynomial $x^3 - 7x^2 + px + q = 0$ have roots $x_1, x_2, x_3$. The sequence formed is geometric with ratio $2$. So it can be assumed that $x_1 = k$, $x_2 = 2k$, $x_3 = 4k$. Or the values $a = k$ and $r = 2$. If ordered $x_1 = a = k$, $x_2 = ar = 2k$, $x_3 = ar^2 = k \cdot 2^2 = 4k$.

The polynomial consecutively has values $a = 1$, $b = -7$, $c = p$, $d = q$. Then the sum of the roots of the polynomial

The value $x_1 = k = 1$ is obtained. Substitute $x = 1$ into the polynomial equation