Solve the equation using the quadratic formula.
$r^{2} + 3 r - 1 = 0$

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Final Answer: The roots of the equation $r^{2} + 3 r - 1 = 0$ are $0.30277563773199456$ and $- 3.302775637731995$ .

Steps

Step 1 ：The given equation is a quadratic equation in the form of $a x^{2} + b x + c = 0$ . The quadratic formula to solve this equation is given by $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ .

Step 2 ：Here, $a = 1$ , $b = 3$ , and $c = - 1$ . We can substitute these values into the quadratic formula to find the roots of the equation.

Step 3 ：Calculate the discriminant, $D = b^{2} - 4 a c = 13$ .

Step 4 ：Substitute the values of a, b, and D into the quadratic formula to find the roots of the equation. The roots are $r 1 = 0.30277563773199456$ and $r 2 = - 3.302775637731995$ .

Step 5 ：Final Answer: The roots of the equation $r^{2} + 3 r - 1 = 0$ are $0.30277563773199456$ and $- 3.302775637731995$ .

Solve the equation using the quadratic formula.r2+3r−1=0

Answer

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Solve the equation using the quadratic formula.
$r^{2} + 3 r - 1 = 0$