Unit 9 – Solving Quadratic Equations
Algebra 2A
WHRHS
2011-2012
Unit 9 – Day F – The Sum & Product of Roots
If you have the Quadratic Equation in Standard Form ax 2  bx  c  0 then the Quadratic
Formula x 
b  b2  4ac
gives you the Solutions/Roots of the equation.
2a
DO NOW: Find the SUM of the Roots & the PRODUCT of the Roots.
*IF r & s are Roots of ax 2  bx  c  0 then r  s 
b
a
AND
*IF divide ax 2  bx  c  0 by a then x 2 
b
c
x 0
a
a
and
rs 
c
a
Unit 9 – Solving Quadratic Equations
Algebra 2A
WHRHS
2011-2012
Examples:
I.
Without solving Find the Sum & Product of the Roots:
1. x 2  5 x  3  0
2. 3x 2  2 x  1  0
3. 5 x 2 
1
1
x 0
2
4
4. 1.2 x 2  2.4 x  3  0
II.
Write the Quadratic Equation with the given Roots:
1. Roots : 5 &  3
2. Roots :
1
2
&
3. Roots :  3
4. Roots : 2  i 7
3
4
WHRHS
Unit 9 – Solving Quadratic Equations
2011-2012
Algebra 2A
Unit 9 Day F HW Page:
W/O solving the equation, Find the Sum & Product of its solutions:
1. 2 x 2  9 x  6  0
2. 6t 2  5t  0
Write a Quadratic Equation, in Standard Form, that has the Given Solutions:
3. 3 & 5
4.
1
4
&
5. 7
6.  7
7. 4  5
8.
2 3
2
1
2
WHRHS
Unit 9 – Solving Quadratic Equations
2011-2012
Algebra 2A
W/O Solving the Equation, Find the Sum and Product of its solutions:
1
1
9. 4 x 2  x   0
3
2
10. 2.5 x 2  5 x  10  0
11. For what values of k will the SUM of the solutions of x 2   k 2  2k  x  12  0 be 8?
12. For what values of k will the PRODUCT of the solutions of
2 x 2  x   4k 2  4k  3  0 be 0?
WHRHS
2011-2012
Unit 9 Day F Part II:
Sums & Products Problems:
Unit 9 – Solving Quadratic Equations
Algebra 2A
1. If
2 is one root of x 2  5x  c  0, find the other root and the value of c.
2. If
3
is one root of 4 x 2  bx  3  0, find the other root and the value of b.
2
3. If
1  i is one root of x 2  bx  2i  0, find the other root and the value of b.
4. One root of 6 x 2  x  k  0 is
1
, find the other root and the value of k .
2
5. One root of kx 2  3x  10  0 is twice the other root , find both roots and the value of k.