Double root

The double root instance occurs when a quadratic equation is the square of a binomial, or when its discriminant is equal to $0$.


Find all solutions to the quadratic equation $3x^2+6x+3=0$.

Plugging the values of $a, b$ and $c$ into the quadratic formula, we get


so this quadratic has a double root of $-1$.

We also could have solved this problem by factoring a $3$ out of the left side and dividing:

$3(x^2+2x+1)=0 \Longrightarrow x^2+2x+1=0$

and now we plug the coefficients into the quadratic formula:


so again, the quadratic has a double root of $-1$.

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