Question

What are the roots of the quadratic equation below?
`3 {x}^(2) + 9x - 2 = 0`

Answer 1

Given:

A quadratic equation is:

`3x^2+9x-2=0`

Find-:

The roots of the quadratic equation

Explanation-:

Use quadratic formula:

`ax^2+bx+c=0`

Roots of the equation,

`x_(1,2)=(-b\pm√(b^2-4ac))/(2a)`

The roots of the given equation are:

`3x^2+9x-2=0`
`\begin{gathered} x_(1,2)=(-b\pm√(b^2-4ac))/(2a) \\ \\ x_(1,2)=(-9\pm√(9^2-4(3)(-2)))/(2(3)) \\ \\ x_(1,2)=(-9\pm√(81-(-24)))/(6) \\ \\ x_(1,2)=(-9\pm√(81+24))/(6) \\ \\ x_(1,2)=(-9\pm√(105))/(6) \end{gathered}`

The roots of a quadratic equation are:

`\begin{gathered} x_(1,2)=(-9\pm√(105))/(6) \\ \\ x_1=(-9+√(105))/(6),x_2=(-9-√(105))/(6) \end{gathered}`
`\begin{gathered} x_1=(-9+√(105))/(6),x_2=(-9-√(105))/(6) \\ \\ x_1=0.2078,x_2=-3.2078 \end{gathered}`

The roots of a quadratic equation are 0.2078 and -3.2078.