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

900005000Step-by-step explanation:...

Use the quadratic formula to find the solutions to

Ответ:

manuellopez1981

04.01.2022

Mathematics

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

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 .

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

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

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