Question

Solve this quadratic equation using the quadratic formula. 3x 2 + 5x + 1 = 0

Answer 1

Answer:

$x=\frac{-\sqrt{13} -5}{6}$ or $x=\frac{\sqrt{13} -5}{6}$

Step-by-step explanation:

The given quadratic equation is

$3x^2+5x+1=0$

When we compare to the general quadratic equation,

$ax^2+bx+c=0$, then we have

$a=3,b=5,c=1$

The quadratic formula is given by,

$x=\frac{-b\pm \sqrt{b^2-4ac} }{2a}$

We substitute the given values into the formula to obtain,

$x=\frac{-5\pm \sqrt{5^2-4(3)(1)} }{2(3)}$

This simplifies to,

$x=\frac{-5\pm \sqrt{25-12} }{2(3)}$

This further simplifies to,

$x=\frac{-5\pm \sqrt{13} }{6}$

We split the plus or minus sign to obtain,

$x=\frac{-\sqrt{13} -5}{6}$ or $x=\frac{\sqrt{13} -5}{6}$