Question

solve the following quadratic equation using the quadratic formula and then choose the correct solution set 8x2-6x+1=0

Answer 1

Answer:

1/4 1/2

Step-by-step explanation:

Answer 2

Answer:

The solutions to the quadratic equation using the quadratic formula will be:

$x=\frac{1}{2},\:x=\frac{1}{4}$

Step-by-step explanation:

Given the equation

$8x^2-6x+1=0$

solving with the quadratic formula

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}$

$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=8,\:b=-6,\:c=1$

$x_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:8\cdot \:1}}{2\cdot \:8}$

as

$\sqrt{\left(-6\right)^2-4\cdot \:8\cdot \:1}=2$

so

$x_{1,\:2}=\frac{-\left(-6\right)\pm \:2}{2\cdot \:8}$

Separating the solution

$x_1=\frac{-\left(-6\right)+2}{2\cdot \:8},\:x_2=\frac{-\left(-6\right)-2}{2\cdot \:8}$

solving

$x_1=\frac{-\left(-6\right)+2}{2\cdot \:\:8}$

    $=\frac{6+2}{2\cdot \:8}$

   $=\frac{8}{16}$

   $=\frac{1}{2}$

and

$x_2=\frac{-\left(-6\right)-2}{2\cdot \:8}$

   $=\frac{6-2}{2\cdot \:\:\:8}$

    $=\frac{4}{16}$

    $=\frac{1}{4}$

Therefore, the solutions to the quadratic equation using the quadratic formula will be:

$x=\frac{1}{2},\:x=\frac{1}{4}$