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Find the roots of $2x^2-12x+22=0$

Step-by-step Solution

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Final Answer

$x=\frac{12+4\sqrt{2}i}{4},\:x=\frac{12-4\sqrt{2}i}{4}$
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Step-by-step Solution

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To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where in this case $a=2$, $b=-12$ and $c=22$. Then substitute the values of the coefficients of the equation in the quadratic formula: $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{12\pm \sqrt{{\left(-12\right)}^2-4\cdot 2\cdot 22}}{2\cdot 2}$

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$x=\frac{12\pm \sqrt{{\left(-12\right)}^2-4\cdot 2\cdot 22}}{2\cdot 2}$

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Learn how to solve problems step by step online. Find the roots of 2x^2-12x+22=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=2, b=-12 and c=22. Then substitute the values of the coefficients of the equation in the quadratic formula: \displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}. Simplifying. To obtain the two solutions, divide the equation in two equations, one when \pm is positive (+), and another when \pm is negative (-). Calculate the power \sqrt{-32} using complex numbers.

Final Answer

$x=\frac{12+4\sqrt{2}i}{4},\:x=\frac{12-4\sqrt{2}i}{4}$

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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 xSolve by factoringSolve by completing the squareSolve by quadratic formula (general formula)Find break even pointsFind the discriminant

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Function Plot

Plotting: $2x^2-12x+22$

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0
a
b
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n
u
v
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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

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