### March 17th 2018 archive

While solving quadratic equations, it’s useful to take a look at the discriminant.

The discriminant is area under the square root in the quadratic formula:

if you have a quadratic equation (equation equal to zero with 3 distinct parts), you can use the quadratic formula to solve. Depending on the answer, we can figure out whether the equation will have 1,2 or 0 solutions.

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Let’s find the discriminant of the equation: $x^2-3x+6=0$

In a quadratic equation, the parent would be $ax^2+bx+c$

following the parent, in our equation, a=1, b=-3, and c=6

using this information we can plug in the numbers to our equation to find the discriminant.

If $b^2-4ac$ is our equation, we just put our numbers we found in the spots of the letters, and simplify.

$b^2-4ac$

$-3^2-4(1)(6)$

$9-4(6)$

$9-24$

$-15$

using this we know that since the discriminant is -15, the original quadratic equation does not have any solutions, and using the quadratic formula would not work.