Question

find the solution set.
$4x^2 - 5x + 1 = 0$
separate the two values with a comma.
enter the correct answer.

Explanation:

Step1: Identify quadratic formula

For $ax^2+bx+c=0$, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Here, $a=4$, $b=-5$, $c=1$

Step2: Calculate discriminant

$\Delta = b^2-4ac = (-5)^2-4(4)(1)=25-16=9$

Step3: Compute square root of discriminant

$\sqrt{\Delta}=\sqrt{9}=3$

Step4: Solve for two roots

First root: $x_1=\frac{-(-5)+3}{2(4)}=\frac{5+3}{8}=\frac{8}{8}=1$
Second root: $x_2=\frac{-(-5)-3}{2(4)}=\frac{5-3}{8}=\frac{2}{8}=\frac{1}{4}$

Answer:

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