Mathematics 2008 JAMB Past Questions - Question 13: If 2x2 -kx-12 is divisible by x-4, find the value of k

Correct Answer

B

Explanation

d f(x) = 6x² - 2x – 4 =0 when at maximum → 3x2- x-2 = 0 → x = 1 To determine if 2x^2 - kx - 12 is divisible by x - 4, we can use the remainder theorem. According to the remainder theorem, if a polynomial is divisible by x - a, then substituting x = a into the polynomial will result in a remainder of zero.In this case, we need to check if 2x^2 - kx - 12 is divisible by x - 4. So, we substitute x = 4 into the polynomial:2(4)^2 - k(4) - 12 = 0Simplifying further:32 - 4k - 12 = 0Combining like terms:20 - 4k = 0To solve for k, we isolate the variable:-4k = -20Dividing both sides by -4:k = 5Therefore, the value of k that makes 2x^2 - kx - 12 divisible by x - 4 is k = 5.