This week in Precalc 11 we learned about discriminant’s. A discriminant is a part of a formula that helps you figure out whether your quadratic formula is going to have no real roots, 1 real root or 2 equal real roots, or if it has 2 unequal real roots. We figure this out by plugging in number into the formula and seeing if it is less than 0, equal to zero, or greater than zero.

• The original formula we get the discriminant from is:

• We take this formula and only use the
• To know which numbers go in place or the variables we look at the quadratic equation.

  NOTE: it must always equal zero, this way you know which one is “a” and “b” and “c”. AND MAKE SURE YOU DON”T FORGET YOUR SIGNS.

Example:

• so just by looking we know that it equals zero.
• and that a=5, b=-8, and c=6
• so now that we know these things we can plug them into our discriminant formula.

• 1)
• 2) 64 – 120
• 3) -56 < 0

• We see that -56 is less than zero which means they’re no real roots.
• If the discriminant was greater than “0” the quadratic would have 2 distinct real roots
• If the discriminant was equal to “0” the quadratic would have 1 real root or 2 equal real roots.