Question

Solve for u.u²-2u-3=0If there is more than one solution, separate them with commas.If there is no solution, click on "No solution."

Answer 1

$\begin{gathered} \text{Given} \\ u^2-2u-3=0 \end{gathered}$

The given equation is in the standard form where a = 1, b = -2, and c = -3.

Use the quadratic formula and substitute the given coefficients. We have the following:

$\begin{gathered} u=\frac{ -b \pm\sqrt{b^2 - 4ac}}{ 2a } \\ u=\frac{ -(-2) \pm\sqrt{(-2)^2 - 4(1)(-3)}}{ 2(1) } \\ u=\frac{2\pm\sqrt{4-(-12)}}{2} \\ u=\frac{2\pm\sqrt{4+12}}{2} \\ u=\frac{ 2 \pm\sqrt{16}}{ 2 } \\ u=\frac{ 2 \pm4\, }{ 2 } \\ \\ u_1=\frac{2+4}{2} \\ u_1=\frac{6}{2} \\ u_1=3 \\ \\ u_2=\frac{2-4}{2} \\ u_2=-\frac{2}{2} \\ u_2=-1 \\ \\ \text{Therefore, the solutions of the given equation is} \\ u=3,-1 \end{gathered}$