Question

the equation
`10 {r}^(2) + 13r - 3 = 0`has solution of the form
`r = \frac{n + √(d) } {m}`use the quadratic formula to solve this equation and find the appropriate integer values of N, M and D. Do not worry about simplifying the D N=____ ; D=_____ M=_____

Answer 1

10r^2 + 13r - 3 = 0

`\begin{gathered} \frac{-b\text{ }\pm\sqrt[]{b^2\text{ - 4ac}}}{2a} \\ \frac{-13\text{ }\pm\sqrt[]{13^2\text{ - 4(10)(-3)}}}{2(10)} \\ \frac{-13\text{ }\pm\sqrt[]{169\text{ +120}}}{20} \\ \frac{-13\text{ }\pm\sqrt[]{289}}{20} \\ \end{gathered}`

a = 10

b= 13

c = -3

a) From the result, we conclude that

N = -13 D = 289 M = 20

b)

`\begin{gathered} \frac{-13\text{ }\pm17}{20} \\ r1\text{ = }\frac{-13\text{ + 17}}{20}\text{ r2 = }\frac{-13\text{ - 17}}{20} \\ r1\text{ = }(4)/(20)\text{ r2 = }(-30)/(20) \\ r1\text{ = }(1)/(5)\text{ r2 =-}\frac{15}{10\text{ }}=-(3)/(2) \\ \end{gathered}`

r1 = 1/5 r2 = -3/2