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# Solve the quadratic equation $3x^2-x-2=0$

## Step-by-step Solution

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###  Videos

$x=1,\:x=-0.666667$
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##  Step-by-step Solution 

Problem to solve:

$3x^2-x-2=0$

Specify the solving method

1

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where in this case $a=3$, $b=-1$ and $c=-2$. Then substitute the values of the coefficients of the equation in the quadratic formula: $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-1\cdot -1\pm \sqrt{{\left(-1\right)}^2-4\cdot 3\cdot -2}}{2\cdot 3}$

Learn how to solve quadratic equations problems step by step online.

$x=\frac{-1\cdot -1\pm \sqrt{{\left(-1\right)}^2-4\cdot 3\cdot -2}}{2\cdot 3}$

Learn how to solve quadratic equations problems step by step online. Solve the quadratic equation 3x^2-x-2=0. To find the roots of a polynomial of the form ax^2+bx+c we use the quadratic formula, where in this case a=3, b=-1 and c=-2. Then substitute the values of the coefficients of the equation in the quadratic formula: \displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}. Simplify \frac{-1\cdot -1\pm \sqrt{{\left(-1\right)}^2-4\cdot 3\cdot -2}}{2\cdot 3}. To obtain the two solutions, divide the equation in two equations, one when \pm is positive (+), and another when \pm is negative (-). Subtract the values 1 and -5.

$x=1,\:x=-0.666667$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve for xFind the rootsSolve by factoringSolve by completing the squareSolve by quadratic formulaFind break even points

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a
b
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n
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x
y
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(◻)
+
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×
◻/◻
/
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e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

~ 0.03 s

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