Solve this quadratic equation using the quadratic formula.3x 2 + 5x + 1 = 0
Accepted Solution
A:
Answer:[tex]x=\frac{-\sqrt{13} -5}{6}[/tex] or [tex]x=\frac{\sqrt{13} -5}{6}[/tex]Step-by-step explanation:The given quadratic equation is [tex]3x^2+5x+1=0[/tex] When we compare to the general quadratic equation,[tex]ax^2+bx+c=0[/tex], then we have [tex]a=3,b=5,c=1[/tex] The quadratic formula is given by,[tex]x=\frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex] We substitute the given values into the formula to obtain,[tex]x=\frac{-5\pm \sqrt{5^2-4(3)(1)} }{2(3)}[/tex] This simplifies to,[tex]x=\frac{-5\pm \sqrt{25-12} }{2(3)}[/tex] This further simplifies to,[tex]x=\frac{-5\pm \sqrt{13} }{6}[/tex] We split the plus or minus sign to obtain, [tex]x=\frac{-\sqrt{13} -5}{6}[/tex] or [tex]x=\frac{\sqrt{13} -5}{6}[/tex]