This document discusses finding the sum and product of the roots of quadratic equations. It provides the formulas for calculating the sum and product of roots without explicitly solving for the individual roots. The sum of the roots is equal to -b/a, and the product of the roots is equal to c/a, where a, b, and c are the coefficients of the quadratic equation in the standard form ax^2 + bx + c = 0. Several examples are worked out applying these formulas. The document also contains exercises asking the reader to find the sum and product of roots for additional quadratic equations using the given coefficients a, b, and c.

1. THE SUM AND
THE PRODUCT
OF ROOTS OF
QUADRATIC
EQUATIONS
Ms. Majesty P. Ortiz

3. −
𝟑
𝟖
+
𝟏
𝟖
−
𝟏
𝟒
−
𝟓
𝟔
+ −
𝟏
𝟔

5. −
𝟏
𝟐
𝟒
𝟐
−
𝟒
𝟑
−
𝟐
𝟑
𝟖
𝟗𝒙 + 𝟐 𝒙 − 𝟐𝒙 𝟐
− 𝟒(𝒙 − 𝟓)(𝒙 + 𝟓)𝒙 𝟐
-25

6. Quadratic Equation
Roots Sum of
Roots
Product of
Roots
𝑥2
+ 7𝑥 + 12 = 0
𝑥2
+ 7𝑥 − 18 = 0
𝑥2
− 5𝑥 − 24 = 0
4𝑥2
+ 𝟖𝑥 + 𝟑 = 0
2𝑥2
+ 8𝑥 − 10 = 0
8𝑥2
− 𝟔𝑥 − 𝟗 = 0

7. x =
−𝒃± 𝒃 𝟐−𝟒𝒂𝒄
𝟐𝒂
𝒙 𝟏 =
−𝒃 + 𝒃 𝟐 − 𝟒𝒂𝒄
𝟐𝒂
𝒙 𝟐 =
−𝒃 − 𝒃 𝟐 − 𝟒𝒂𝒄
𝟐𝒂

8. Sum of the Roots of Quadratic Equation
𝒙 𝟏 + 𝒙 𝟐 =
−𝒃
𝒂
Product of the Roots of Quadratic Equation
𝑥1 ⋅ 𝑥2 =
𝑐
𝑎

9. 1) 𝒙 𝟐
−𝟐𝒙 − 𝟑 = 𝟎
2) 𝟔𝒙 𝟐
+ 𝟏𝟐𝒙 + 𝟒 = 𝟎
3) 𝟗𝒙 𝟐
− 𝟐𝟓 = 𝟎

10. Use the values of a, b, and c of each of the following
equations in determining the sum and the product of its
roots.
1. 𝒙 𝟐
+𝟒𝒙 + 𝟑 = 𝟎
2. 𝟔𝒙 𝟐
+ 𝟏𝟐𝒙 − 𝟏𝟖 = 𝟎
3. 𝒙 𝟐
+𝟒𝒙 − 𝟐𝟏 = 𝟎
4. 𝟐𝒙 𝟐
+ 𝟑𝒙 − 𝟐 = 𝟎
5. 𝟑𝒙 𝟐
− 𝟏𝟎𝒙 − 𝟖 = 𝟎

11. SUM PRODUCT
1. - 4 3
2. -2 -3
3. -4 -21
4. −
𝟑
𝟐
-1
5.
𝟏𝟎
𝟑
−
𝟖
𝟑

12. A.Without solving for the
roots, find the sum and
product of the roots of
each quadratic equation.
1. 𝒙 𝟐
+ 𝟓𝒙 − 𝟔 = 𝟎
2. 𝒙 𝟐
+𝟏𝟓𝒙 + 𝟓𝟒 = 𝟎
3. 𝒙 𝟐
+𝟖𝒙 = −𝟏𝟑
4. 𝟑𝒙 𝟐
+ 𝟔𝒙 − 𝟑 = 𝟎
5. 𝟒𝒙 𝟐
+ 𝟖𝒙 + 𝟑 = 𝟎
B.Write a quadratic
equation with integral
coefficients whose sum
and product of roots are
given.
1.
𝟏
𝟐
𝒂𝒏𝒅 −
𝟐
𝟑
2. −
𝟑
𝟒
𝒂𝒏𝒅
𝟓
𝟔
3. 0 and 6