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

User Miss
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1 Answer

2 votes

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.

User Paul Stengel
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