Question

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

Answer 1

Answer: x= 5-√10 / 3

x= 5 + √10/ 3

Step-by-step explanation:

-(-10) +- √(-10)^2 -4 x 3 x 5 / 2x 3

x= 10 +- √100-60 / 6

x=10 +- √ 40

simplify to x = 10 +- 2√10 / 6

simplify both equations now

divide both equations by 2 which gives the answer.

Answer 2

Answer:

$x=\frac{5+ \sqrt{10}}{3}\,,\,\frac{5- \sqrt{10}}{3}$

Step-by-step explanation:

Let $ax^2+bx+c=0$ be a quadratic equation where a , b , c are coefficients and a ≠ 0.

Using quadratic formula, roots are given by $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

On comparing equation $3x^2-10x+5=0$ with equation $ax^2+bx+c=0$ , we get $a=3\,,\,b=-10\,,\,c=5$

First , we will find $b^2-4ac$ :

$(-10)^2-4(3)(5)=100-60=40$

So, $\sqrt{b^2-4ac}=\sqrt{40}=2\sqrt{10}$

Now, using quadratic formula, we will find roots of the equation .

$\begin{align*}\displaystyle x &=\frac{10\pm 2\sqrt{10}}{6}\\\displaystyle &=\frac{5\pm \sqrt{10}}{3}\\\displaystyle &=\frac{5+ \sqrt{10}}{3}\,,\,\frac{5- \sqrt{10}}{3}\\ \end{align*}$