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