Question

for the few questions in this set, you will see the quadratic formula. soon, you will need to answer the questions without this reminder.
$x = \frac{ -b \pm \sqrt{b^2 - 4ac} }{ 2a }$
for $ax^2 + bx + c = 0$

solve for x. write both solutions, separated by a comma.
$6x^2 - x - 5 = 0$
enter the correct answer.

Explanation:

Step1: Identify a, b, c values

From $6x^2 - x - 5 = 0$, we get $a=6$, $b=-1$, $c=-5$.

Step2: Calculate discriminant

$\Delta = b^2 - 4ac = (-1)^2 - 4(6)(-5) = 1 + 120 = 121$

Step3: Substitute into quadratic formula

$$ x = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{-(-1) \pm \sqrt{121}}{2(6)} = \frac{1 \pm 11}{12} $$

Step4: Solve for both roots

First root: $x = \frac{1 + 11}{12} = \frac{12}{12} = 1$
Second root: $x = \frac{1 - 11}{12} = \frac{-10}{12} = -\frac{5}{6}$

Answer:

$1, -\frac{5}{6}$