Question 10

Explanation

The polynomial $x^3 - 12x^2 + (p + 4)x - (p + 8) = 0$ with $a = 1$, $b = -12$, $c = p + 4$, and $d = -(p + 8)$. The roots $x_1, x_2, x_3$ form an arithmetic sequence with common difference $2$. So $x_1 = k$, $x_2 = k + 2$, $x_3 = k + 4$.

Determining the value of $k$ using the sum of roots

So the roots are $x_1 = 2$, $x_2 = 4$, $x_3 = 6$. Then determining the value of $p$ from the product of its roots

So the value of $p - 36 = 40 - 36 = 4$.