Mathematics 2019 JAMB Past Questions - Question 24: Find a positive value of p if the expression 2x2-px + p leaves a reminder 6 when divided by x –p

Correct Answer

B

Explanation

To find the positive value of \( p \) such that the expression \( 2x^2 - px + p \) leaves a remainder of 6 when divided by \( x - p \), we can use the remainder theorem.According to the remainder theorem, if a polynomial \( f(x) \) is divided by \( x - p \), then the remainder is \( f(p) \).In this case, we want the remainder to be 6. So, we need to find a positive value of \( p \) such that when \( 2x^2 - px + p \) is evaluated at \( x = p \), the result is 6.Substituting \( x = p \) into the expression gives:\[ 2p^2 - p^2 + p = 6 \]Simplifying this equation gives:\[ p^2 + p = 6 \]\[ p^2 + p - 6 = 0 \]Now, we need to solve this quadratic equation to find the value of \( p \). Factoring the quadratic equation gives:\[ (p + 3)(p - 2) = 0 \]So, the solutions are \( p = -3 \) and \( p = 2 \). However, we are looking for a positive value of \( p \), so the correct answer is \( p = 2 \).Therefore, the positive value of \( p \) is 2, so the answer is B. 2.