163k views
1 vote
Given 5n² + 6n + 7 = n² - 4n : a. Find the value of the discriminant. b. State the number and type of roots/solutions/zeros.[2 real, 2 imaginary, 1 real]

1 Answer

5 votes

\bf 5n^2+6n+7=n^2-4n\implies 5n^2+6n+7-n^2+4n=0 \\\\\\ 4n^2+10n+7=0\\\\ -------------------------------\\\\ \begin{array}{llccll} &{{ 4}}x^2&{{ +10}}x&{{ +7}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array} \\\\\\ discriminant\implies b^2-4ac= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases}

if you get a positive value, that means 2 real solutions
if you get 0, means 1 real solution only
if you get a negative value, is an imaginary root solution, same as saying no solution.
User Joshweir
by
7.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories