The teacher has written an equation of the form on the board, where is a quadratic, 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 3.''

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 31, 2021

#1**+2 **

**The teacher has written an equation of the form on the board, where is a quadratic, 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 3.''**

**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.**

\(\begin{array}{|rcll|} \hline 4x^2+ax-24&=& 0 \\ \hline \dfrac{-24}{4} &=& r_1*r_2 \quad | \quad r_1 = 3 \\\\ \dfrac{-24}{4} &=& 3*r_2 \\\\ r_2 &=& \dfrac{-24}{12} \\\\ \mathbf{r_2} &=& \mathbf{-2} \\ \hline \dfrac{a}{4} &=& - (r_1+r_2) \\\\ \dfrac{a}{4} &=& - (3-2) \\\\ \mathbf{ a } &=& \mathbf{ -4 } \\ \hline \end{array}\)

\(4x^2-4x-24\)

heureka May 31, 2021