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

`x_1=(5-√(10))/(3)\approx 0.61,\\ \\x_2=(5+√(10))/(3)\approx 2.72.`

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=(-b-√(D))/(2a)=(-(-10)-√(40))/(2\cdot 3)=(10-2√(10))/(6)=(5-√(10))/(3),\\ \\x_2=(-b+√(D))/(2a)=(-(-10)+√(40))/(2\cdot 3)=(10+2√(10))/(6)=(5+√(10))/(3).`

Approximate the solution to the nearest hundredth:

`x_1=(5-√(10))/(3)\approx 0.61,\\ \\x_2=(5+√(10))/(3)\approx 2.72.`

Answer 2

`n_1=2.72\\n_2=0.61`

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`