Question

Solve the following quadratic equation using the quadratic formula and then choose the correct solution set.

8x2 - 6x + 1 = 0

{1/8,5/8 }
{1/4, 1/2}
{±1/2}

Answer 1

8x2 - 6x + 1 = 0
(2x-1)(4x-1) = 0

2x-1 = 0
x=1/2

4x-1=0
x = 1/4

answer {1/4, 1/2}(second choice)

Answer 2

Answer: The the correct solution set is (B) $\{\dfrac{1}{4},\dfrac{1}{2}\}.$

Step-by-step explanation:  The given equation is

$8x^2-6x+1=0.~~~~~~~~~~~~~~(i)$

We are to choose the correct solution set after solving the above equation by using quadratic formula.

We know that, the solution set for the quadratic equation $ax^2+bx+c=0,~a\neq 0$ is given by

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}.$

In the given equation (i), we have

$a=8,~~b=-6,~~c=1.$

Therefore, the solution set will be given by

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\\Rightarrow x=\dfrac{-(-6)\pm \sqrt{(-6)^2-4\times 8\times 1}}{2\times 8}\\\\\\\Rightarrow x=\dfrac{6\pm\sqrt{36-32}}{16}\\\\\\\Rightarrow x=\dfrac{6\pm\sqrt{4}}{16}\\\\\\\Rightarrow x=\dfrac{6\pm 2}{16}\\\\\\\Rightarrow x=\dfrac{6+2}{16},~~\dfrac{6-2}{16}\\\\\\\Rightarrow x=\dfrac{8}{16},~~\dfrac{4}{16}\\\\\\\Rightarrow x=\dfrac{1}{2},~~\dfrac{1}{4}.$

Thus, the correct solution set is (B) $\{\dfrac{1}{4},\dfrac{1}{2}\}.$