2.5 (Day 2) Discriminant & Finding the Equation

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

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

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

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

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

Ex 5) Find a monic quadratic equation whose roots are 0 and –3 x 2 – (sum)x + product = 0 sum: 0 + –3 = –3 product: (0)(–3) = 0 x 2 – (–3)(x) + 0 = 0 x 2 + 3x = 0 equation  better have = sign

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

Homework #212 Pg – 51 odd & WS 11–13