Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Eigenvalues and eigenvectors wikipedia , lookup
Root of unity wikipedia , lookup
System of linear equations wikipedia , lookup
Fundamental theorem of algebra wikipedia , lookup
System of polynomial equations wikipedia , lookup
Factorization wikipedia , lookup
Elementary algebra wikipedia , lookup
Quadratic form wikipedia , lookup
History of algebra wikipedia , lookup
Cubic function wikipedia , lookup
6.3 Solving Quadratic Equations by Factoring Write a quadratic equation with given roots Roots or Zeros of the Quadratic Equation The Roots or Zeros of the Quadratic Equation are the points where the graph hits the x axis. The zeros of the functions are the input that make the equation equal zero. x 4x 3 0 Roots are 4,-3 To solve a Quadratic Equation Make one side zero. x 2 5x x 2 5x 0 Then factor then set each factor to zero x x 5 0 x 0; x 5 0 x 0; x 5 Solve x 2 28 3x Solve x 2 28 3 x x 2 3 x 28 0 Solve x 2 28 3 x x 2 3 x 28 0 x 7 x 4 0 Solve x 2 28 3x x 2 3 x 28 0 x 7 x 4 0 x 7 0; x 4 0 Solve x 2 28 3 x x 2 3 x 28 0 x 7 x 4 0 x 7 0; x 4 0 x 7; x 4 Solve 3x 2 5 x 2 3x 2 5 x 2 0 Solve 3x 2 5 x 2 3x 2 5 x 2 0 Multiply the ends together and find what adds to the coefficient of the middle term 3(2) 6 (6)(1) 6 (6) (1) 5 Solve 3x 2 5 x 2 3x 2 5 x 2 0 Use -6 and 1 to break up the middle term 3x 6 x 1x 2 0 2 Solve Use group factoring to factor, first two terms and then the last two terms 3x 6 x 1x 2 0 2 3 x x 2 1 x 2 0 x 23x 1 0 3x 2 5 x 2 Solve 3x 2 5 x 2 0 3x 6 x 1x 2 0 2 3 x x 2 1 x 2 0 x 23x 1 0 x 2; 3 x 1 x 2; 1 x 3 How to write a quadratic equation with roots Given r1,r2 the equation is (x - r1)(x - r2)=0 Then foil the factors, x2 - (r1 + r2)x+(r1· r2)=0 How to write a quadratic equation with roots Given r1,r2 the equation is (x - r1)(x - r2)=0 Then foil the factors, x2 - (r1 + r2)x+(r1· r2)=0 Roots are -2, 5 Equation x2 - (-2+5)x+(-2)(5)=0 x2 - 3x -10 = 0 How to write a quadratic equation with roots Roots are ¼, 8 Equation x2 -(¼+8)x+(¼)(8)=0 x2 -(33/4)x + 2 = 0 Must get rid of the fraction, multiply by the common dominator. 4 4x2 - 33x + 8 = 0 Homework Page 304 # 15 – 41 odd Homework Page 304 # 14 – 42 even