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.
+26367 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.
\(\begin{array}{|rcll|} \hline 4x^2+ax-24&=& 0 \\ \hline \dfrac{-24}{4} &=& r_1*r_2 \quad | \quad r_1 = 3 \\\\ \dfrac{-24}{4} &=& 3*r_2 \\\\ r_2 &=& \dfrac{-24}{12} \\\\ \mathbf{r_2} &=& \mathbf{-2} \\ \hline \dfrac{a}{4} &=& - (r_1+r_2) \\\\ \dfrac{a}{4} &=& - (3-2) \\\\ \mathbf{ a } &=& \mathbf{ -4 } \\ \hline \end{array}\)
\(4x^2-4x-24\)
