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.
$4x^2 - x - 3 = 0$
enter the correct answer.

Explanation:

Step1: Identify a, b, c values

From $4x^2 - x - 3 = 0$, we get $a=4$, $b=-1$, $c=-3$.

Step2: Compute discriminant

$\sqrt{b^2 - 4ac} = \sqrt{(-1)^2 - 4(4)(-3)} = \sqrt{1 + 48} = \sqrt{49} = 7$

Step3: Apply quadratic formula

First solution: $x = \frac{-(-1) + 7}{2(4)} = \frac{1 + 7}{8}$
Second solution: $x = \frac{-(-1) - 7}{2(4)} = \frac{1 - 7}{8}$

Step4: Simplify solutions

First solution: $\frac{8}{8} = 1$
Second solution: $\frac{-6}{8} = -\frac{3}{4}$

Answer:

$1, -\frac{3}{4}$