1. 2.5 (Day 2) Discriminant & Finding the Equation
Today’s Date:
10/17/17

2. Discriminant
Discriminant: tells the nature of the roots (the part under the radical) Three Possibilities:
2 = real roots
(1 double root)
2 ≠ real roots
2 complex conjugate roots
(non-real)

3. Ex 1) Use the discriminant to determine the nature of the roots
a = 2, b = –1, c = –15
2 ≠ real roots
Note: Discriminant doesn’t give us the actual roots, just the nature of them

4. Ex 2) Use the discriminant to determine the nature of the roots
a = 4, b = –20, c = 25
2 = real roots

5. Ex 3) Use the discriminant to determine the nature of the roots
TOO
Ex 3) Use the discriminant to determine the nature of the roots
a = 1, b = 4, c = 13
2 complex conjugate roots

6. Sum-Product Rule Given 2 roots, we can write the quadratic equation:
x2 – (sum)x + product = 0
leading coeff = 1
Ex 4) Determine a monic quadratic eqtn if the sum of its roots is –2 and the product of its roots is –8.
x2 – (sum)x + product = 0
x2 – (–2)(x) + –8 = 0
x2 + 2x – 8 = 0

7. Ex 5) Find a monic quadratic equation whose roots are 0 and –3
x2 – (sum)x + product = 0
sum: –3 = –3
product: (0)(–3) = 0
x2 – (–3)(x) + 0 = 0
x2 + 3x = 0
equation  better have = sign

8. Ex 6) Determine k so that roots are equal real roots.
2 = real  discriminant = 0
a = 6, b = k, c = 5

9. Homework
#212 Pg – 51 odd & WS 11–13