This week in Precalc 11, we mostly focused on reviewing for our solving quadratic equations test but we did learn one thing before our test.

In the picture above is the quadratic formula, the highlighted area is called the discriminant. The discriminant can be helpful in many ways while solving a quadratic equation. From what we know, the discriminant is able to find the nature of the root. Whether its a real root, unreal root, irrational or rational, it serves a big purpose.

We know that if …

X = 0 : there is one real root

X > 0 : there are two real roots

X < 0 : there are no real roots

Ex : pg 232, #4b

$3x^2 + 7x - 2 = 0$

$b^2 - 4ac$

$(7)^2 - 4(3)(-2)$

$49 + 24 = 73$

Since we know that the value of this discriminant is 73 (bigger than 0), this equation has 2 real roots. We also know that this is irrational since it’s a prime number

This lesson was very short but it showed us how useful the discriminant is. During our unit test, I found out the discriminant of one equation and it helped me find out that there were no real roots which made it less time consuming for me.