Question

Solve each equation using the quadratic formula. Find the exact solution, then approximate the solution to the nearest hundredth.

3x^2 - 10x + 5 = 0

Answer 1

Answer:

$n_1=2.72\\n_2=0.61$

Step-by-step explanation:

 To solve this problem you  must apply the proccedure shown below:

1. You have that the quadratic formula is:

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

2. To solve the quadratic equation you must substitute the values. So, you have that:

$a=3\\b=-10\\c=5$

Then you have:

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

3. Therefore, you obtain the following result:

$x_1=2.72\\x_2=0.61$

Answer 2

Answer:

$x_1=\dfrac{5-\sqrt{10}}{3}\approx 0.61,\\ \\x_2=\dfrac{5+\sqrt{10}}{3}\approx 2.72.$

Step-by-step explanation:

The equation $3x^2-10x+5=0$ is quadratic equation. Find the discriminant:

$D=b^2-4ac=(-10)^2-4\cdot 3\cdot 5=100-60=40.$

Then the exast solutions of the equation are

$x_1=\dfrac{-b-\sqrt{D}}{2a}=\dfrac{-(-10)-\sqrt{40}}{2\cdot 3}=\dfrac{10-2\sqrt{10}}{6}=\dfrac{5-\sqrt{10}}{3},\\ \\x_2=\dfrac{-b+\sqrt{D}}{2a}=\dfrac{-(-10)+\sqrt{40}}{2\cdot 3}=\dfrac{10+2\sqrt{10}}{6}=\dfrac{5+\sqrt{10}}{3}.$

Approximate the solution to the nearest hundredth:

$x_1=\dfrac{5-\sqrt{10}}{3}\approx 0.61,\\ \\x_2=\dfrac{5+\sqrt{10}}{3}\approx 2.72.$