The teacher has written a quadratic on the board, but Heather can't read the linear term. She can see that the quadratic term is 4x^2 and that the constant is -24. She asks her neighbor, Noel, what the linear term is. Noel decides to tease her and just says, ``One of the roots is 4.'' Heather then says, ``Oh, thanks!'' She then correctly writes down the linear term. What was the linear term? Include entire term, not simply the coefficient

Guest May 11, 2019

#1**+3 **

The quadratic has this form: 4x^{2} + ax - 24 = 0 and the problem is to find the value of a.

Since one of the roots is 4, replace x with 4 in the quadratic:

4x^{2} + ax - 24 = 0 ---> 4(4)^{2} + a(4) - 24 = 0 ---> 4(16) + 4a - 24 = 0 ---> 64 + 4a - 24 = 0

---> 4a + 40 = 0 ---> 4a = -40 ---> a = -10

So, the linear term is -10x.

geno3141 May 11, 2019