Questions: Fill in the blanks so that the resulting statement is true. In order to solve (8 x^2+7 x-1=0) by the quadratic formula, use (a=) , (b=) , and (c=) .

Transcript text: Fill in the blanks so that the resulting statement is true. In order to solve $8 x^{2}+7 x-1=0$ by the quadratic formula, use $a=$ $\square$ , $\mathrm{b}=$ $\square$ , and $c=$ $\square$ .

Solution

Solution Steps

Step 1: Identify the coefficients of the quadratic equation

The given quadratic equation is $ax^2 + bx + c = 0$ with $a = 8$, $b = 7$, and $c = -1$.

Step 2: Calculate the discriminant

The discriminant $D$ is calculated as $D = b^2 - 4ac = 7^2 - 4_8_-1 = 81$.

Step 3: Since the discriminant is positive, there are two distinct real roots.

Step 4: Apply the quadratic formula

The roots of the quadratic equation can be found using the formula $x = \frac{-b \pm \sqrt{D}}{2a}$. Substituting the values, we get $x_1 = (0.12+0j)$ and $x_2 = (-1+0j)$.