Question

How many real zeros does the

following quadratic function have?
f(x) = 6x² + 11x + 5
Remember the quadratic formula: x = =b+√b²-4ac
2a
A. no real zeros
B. one real zero
C. two real zeros

Answer 1

`\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{6}x^2\stackrel{\stackrel{b}{\downarrow }}{+11}x\stackrel{\stackrel{c}{\downarrow }}{+5} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ 11^2 - 4(6)(5)\implies 121-120\implies 1\qquad \textit{two real solutions}`