Question

solve using the quadratic formula.
$5j^2 + j - 1 = 0$
write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
$j = \square$ or $j = \square$

Explanation:

Step1: Identify quadratic coefficients

For $5j^2 + j - 1 = 0$, we have $a=5$, $b=1$, $c=-1$.

Step2: Recall quadratic formula

The quadratic formula is $j = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Step3: Calculate discriminant

$$\Delta = b^2 - 4ac = 1^2 - 4(5)(-1) = 1 + 20 = 21$$

Step4: Substitute into formula

$$j = \frac{-1 \pm \sqrt{21}}{2(5)} = \frac{-1 \pm \sqrt{21}}{10}$$

Step5: Compute decimal values

$\sqrt{21} \approx 4.583$, so:
$j = \frac{-1 + 4.583}{10} \approx 0.36$
$j = \frac{-1 - 4.583}{10} \approx -0.56$

Answer:

$j = \frac{-1 + \sqrt{21}}{10}$ or $j = \frac{-1 - \sqrt{21}}{10}$
or as decimals: $j \approx 0.36$ or $j \approx -0.56$