Questions: Consider the following quadratic equation: 4 y^2 - 4 y = -1 Step 1 of 2: Find the values of a, b, and c that should be used in the quadratic formula to determine the solution of the quadratic equation.

Consider the following quadratic equation:
4 y^2 - 4 y = -1

Step 1 of 2: Find the values of a, b, and c that should be used in the quadratic formula to determine the solution of the quadratic equation.

Transcript text: Consider the following quadratic equation: \[ 4 y^{2}-4 y=-1 \] Step 1 of 2: Find the values of $a, b$, and $c$ that should be used in the quadratic formula to determine the solution of the quadratic equation.

Solution

Solution Steps

Step 1: Identify the coefficients of the quadratic equation

The given quadratic equation is of the form $ax^2 + bx + c = 0$, where $a = 4$, $b = -4$, and $c = -1$.

Step 2: Calculate the discriminant

The discriminant ($\Delta$) of the quadratic equation is calculated as $b^2 - 4ac$. For our equation, $\Delta = -4^2 - 4_4_-1 = 32$.

Step 3: Determine the nature of the roots

Since the discriminant is positive ($\Delta > 0$), there are two distinct real roots.

Step 4: Calculate the roots using the quadratic formula

The roots of the quadratic equation can be found using the formula $x = \frac{-b \pm \sqrt{\Delta}}{2a}$. Substituting the values, we get the roots as $x_1 = (1.21+0j)$ and $x_2 = (-0.21+0j)$.