Question

question 17 of 25
use the quadratic formula to find the solutions to the quadratic equation below. check all that apply.
$4x^2 - x - 5 = 0$

a. $\frac{3}{2}$
b. $-1$
c. $\frac{2}{3}$
d. $-\frac{4}{5}$
e. $\frac{5}{4}$
f. $1$

Explanation:

Step1: Recall Quadratic Formula

For a quadratic equation \(ax^2 + bx + c = 0\), the solutions are given by \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). In the equation \(4x^2 - x - 5 = 0\), we have \(a = 4\), \(b=-1\), and \(c = -5\).

Step2: Calculate the Discriminant

First, calculate the discriminant \(D=b^2 - 4ac\). Substituting the values, we get \(D=(-1)^2-4\times4\times(-5)=1 + 80 = 81\).

Step3: Find the Solutions

Now, find the solutions using the quadratic formula. \(x=\frac{-(-1)\pm\sqrt{81}}{2\times4}=\frac{1\pm9}{8}\).

• For the plus sign: \(x=\frac{1 + 9}{8}=\frac{10}{8}=\frac{5}{4}\).
• For the minus sign: \(x=\frac{1-9}{8}=\frac{-8}{8}=-1\).

Answer:

B. \(-1\), E. \(\frac{5}{4}\)