Question

Select the two values of x that are roots of this equation 3x^2 + 1 =5x

Answer 1

x = 1.434 and x=0.232

Explanation:

To find the root of the equation stated above we need to:

(1) Write the polynomial equation with zero on the right hand side:

`3x^(2) + 1 = 5x` ⇒
`3x^(2) -5x + 1 = 0`

(2) Divide the whole equation by 3

`3x^(2) -5x + 1 = 0` ⇒
`x^(2) -(5)/(3)x + (1)/(3)= 0`

(3) Use the quadratic formula to solve the quadratic equation:

The quadratic formula states that the two solutions for a quadratic equation is given by:

`\frac{-b±\sqrt{b^(2) - 4ac}}{2a}` (1)

In this case, a = 1, b =
`-(5)/(3), c= (1)/(3)`

Substituiting a, b and c in equation (1) We get:

`\frac{-(5)/(3)±\sqrt{(-(5)/(3))^(2) - 4(1)((1)/(3))}}{2(1)}` (1)

The two solutions are:

x = 1.434 and x=0.232