Mathematics 2022 JAMB Past Questions - Question 11: The expression px³ +2qx² +24 has x-1 and x+2 as factors. The values of p and q are respectively?

Correct Answer

A

Explanation

If (x - 1) and (x + 2) are factors of the expression px³ + 2qx² + 24, we can use the factor theorem to find the values of p and q.According to the factor theorem, if (x - a) is a factor of a polynomial, then the polynomial will be equal to zero when x = a.Using this information, we can set up two equations:1. When x = 1:  p(1)³ + 2q(1)² + 24 = 0  p + 2q + 24 = 02. When x = -2:  p(-2)³ + 2q(-2)² + 24 = 0  -8p + 8q + 24 = 0Now, we can solve these two equations simultaneously to find the values of p and q.From equation 1, we have:p + 2q + 24 = 0 ----(1)From equation 2, we have:-8p + 8q + 24 = 0 ----(2)Multiplying equation 1 by 4, we get:4p + 8q + 96 = 0 ----(3)Adding equation 2 and equation 3, we have:-8p + 8q + 24 + 4p + 8q + 96 = 0-4p + 16q + 120 = 0Dividing the equation by -4, we get:p - 4q - 30 = 0 ----(4)Now, we have two equations:p + 2q + 24 = 0 ----(1)p - 4q - 30 = 0 ----(4)Solving these equations simultaneously, we find:p = -6q = 9Therefore, the values of p and q are -6 and 9, respectively.