Download 6.3 Solving Quadratic Equations by Factoring

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  4x  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  23x  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  23x  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