Do Now – Take out your homework. Take You have 5 minutes. How can you find out if a quadratic equation has only one solution without solving the equation? How many solutions does y =5x2 - 10x + 5 have? Explain.

Focus Question: How can we find missing coefficients in a quadratic equation? What are sum and product of roots? November 20, 2013

Missing coefficients: Imaginary – “< 0” Real and Unequal – “> 0” Equal roots - “= 0 ”

4x2 – nx + 1 = 0 For which value of n will the roots be equal? What does my discriminant need to be? b2 – 4ac a = 4, b = n c = 1 n2 - 4(4)(1) n = 4

3x2 – 6x + n < 0 For which value of n will the roots be imaginary? b2 – 4ac a = 3 b = -6 c= n 36 – 4(3)(n) n>3

nx2 – 6x + 5 > 0 For which value of n will the roots be real and unequal? b2 - 4ac a = n, b = -6 c = 5 (-6)2 - 4(n)(5) 36 – 20n n < 9/5

Sum and Product of Roots If the roots of ax2 + bx + c with a ≠ 0 are s1 and s2, then:

Find the sum of the roots Find the product of the roots

PRACTICE

Project – Get into groups Begin working on mini project.