Question

Us the quadratic formula to solve 3x^2+5x+2

Answer 1

x = -2/3, -1

Explanation:

Solve the equation for x by finding a, b, and c of the quadratic then apply the quadratic formula.

Answer 2

For this case we have a quadratic equation of the form
`ax ^ 2 + bx + c = 0`, where:

`a = 3\\b = 5\\c = 2`

The solution of the equation is determined by the quadratic formula, which is given by:

`x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}`

Substituting the values in the formula we have:

`x = \frac {-5 \pm \sqrt {5 ^ 2-4 (3) (2)}} {2 (3)}\\x = \frac {-5 \pm \sqrt {(25-24)}} {6}\\x = \frac {-5 \pm \sqrt {1}} {6}\\x = \frac {-5 \pm1} {6}`

So:

`x_ {1} = \frac {-5 + 1} {6} = \frac {-4} {6} = \frac {-2} {3}\\x_ {2} = \frac {-5-1} {6} = \frac {-6} {6} = - 1`

Answer:

The roots are:

`x_ {1} = \frac {-2} {3}\\x_ {2} = - 1`