Question

Use the quadratic formula to find the solutions to the equation. 3x^2- 10x+ 5 = 0

Answer 1

Answer:

$x =\frac{5}{3} \pm \frac{\sqrt{10}}{3} \\\\x=2.72076\\x=0.612574$

Step-by-step explanation:

The quadratic equation is:

$3x^2 - 10x + 5 = 0$

The roots (solutions) of a quadratic equation of the form
$a^2 + bx + c = 0$

are

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

in this case we have a = 3, b = -10, and c = 5

So, substituting for a, b and c we get

$x = \frac{ -(-10) \pm \sqrt{(-10)^2 - 4(3)(5)}}{ 2(3) }$

$x = \frac{ 10 \pm \sqrt{100 - 60}}{ 6 }$

$x = \frac{ 10 \pm \sqrt{40}}{ 6 }$

Simplifying we get

$x = \frac{ 10 \pm 2\sqrt{10}\, }{ 6 }\\\\x = \frac{ 10 }{ 6 } \pm \frac{2\sqrt{10}\, }{ 6 }\\\\x = \frac{ 5}{ 3 } \pm \frac{ \sqrt{10}\, }{ 3 }\\\\\frac{ 5}{ 3 } + \frac{ \sqrt{10}\, }{ 3 } = 2.72076$  (First root/solution)

$\frac{ 5}{ 3 } - \frac{ \sqrt{10}\, }{ 3 } = 0.612574$  (Second root/solution)