Question

The equation t2 + 1t - 30 = 0 has solutions of the formt=N+/- DM(A) Use the quadratic formula to solve this equation and find the appropriate integer values of N,M andD. Do not worry about simplifying the VD yet in this part of the problem.N=D=M=(B) Now simplify the radical and the resulting solutions. Enter your answers as a list of integers or reducedfractions, separated with commas. Example: -5/2,-3/4

Answer 1

Given:

`\begin{gathered} t^2+1t-30=0 \\ t=\frac{N\pm\sqrt[]{D}}{M} \end{gathered}`

Find: N,D,M and value of t.

Sol:.

Quadratic formula:

`\begin{gathered} ax^2+bx+c=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}`
`\begin{gathered} t^2+1t-30=0 \\ a=1 \\ b=1 \\ c=-30 \end{gathered}`
`\begin{gathered} t=\frac{-1\pm\sqrt[]{1^2-4(1)(-30)}}{2(1)} \\ t=\frac{-1\pm\sqrt[]{1+120}}{2} \\ t=\frac{-1\pm\sqrt[]{121}}{2} \end{gathered}`

So

`\begin{gathered} \frac{-1\pm\sqrt[]{121}}{2}=\frac{N\pm\sqrt[]{D}}{M} \\ N=-1 \\ D=121 \\ M=2 \end{gathered}`

(B)

Value of "t"

`\begin{gathered} t=\frac{-1\pm\sqrt[]{121}}{2} \\ t=(-1\pm11)/(2) \\ t=(-1+11)/(2),t=(-1-11)/(2) \\ t=(10)/(2),t=(-12)/(2) \\ t=5,-6 \end{gathered}`

So value of t is 5,-6