This powerpoint presentation discusses or talks about the topic or lesson Roots and Coefficients of Quadratic Equations. It also discusses and explains the rules, steps and examples of Roots and Coefficients of Quadratic Equations

1. ROOTS AND
COEFFICIENTS OF
QUADRATIC
EQUATIONS

2. DISCRIMINANT
The radicand (b2
− 4ac) in the quadratic
formula

3. USING THE
DISCRIMINANT
Given a quadratic equation in the form of
ax2 + bx + c = 0, where a, b, and c are real
numbers and a≠0. We can determine the
number and type of solutions of a
quadratic equation, by evaluating the
discriminant

4. USING THE
DISCRIMINANT
1. If b2
− 4ac > 0, the equation has two
real solutions. Both will be rational if
the discriminant is a perfect square or
irrational, otherwise

5. USING THE
DISCRIMINANT
2. If b2
− 4ac = 0, the equation has only
one solution which will be a rational
number

6. USING THE
DISCRIMINANT
3. If b2
− 4ac < 0, the equation has no
real number solution

7. USING THE
DISCRIMINANT
Example: 16x2 - 8x + 1 = 0
b2
− 4ac = (-8)2 – 4(16)(1)
= 64 – 64
= 0
Because the discriminant is 0, the equation has
only solution

8. RELATION OF ROOTS
1. The sum of the roots is the additive
inverse of the quotient of b and a
r1 + r2 = -
b
a

9. RELATION OF ROOTS
2. The product of the roots is the
quotient of c and a
r1 - r2 =
c
a

10. RELATION OF ROOTS
The relations that exist between the
roots of a quadratic equation which can
be used in checking the validity of the
roots can be of best use in deriving the
quadratic equation

11. General Form: ax2 + bx + c = 0
Expressed in the form of Multiplication
Property of Equality:
x2 +
b
a
x +
c
a
= 0

12. RULE
To derive the quadratic equation when
the two roots are given, subtract each
root from x to get the corresponding
linear factors and equate the product of
the linear factors to zero

13. Example: x2 – 3x – 28 = 0
Solution:
(x-7) (x+4) = 0
x-7 = 0 or x+4=0
x=7 (root 1) x=-4 (root 2)

14. Example: x2 – 3x – 28 = 0
Check whether the roots are correct:
r1 + r2 = -
b
a
and r1 - r2 =
c
a
(7) + (-4) =
(−3)
1
(7) (-4) = -
28
1
3 = 3 True -28 = -28 True