This document discusses solving quadratic equations and properties of their roots. It covers: 1) Finding the sum and product of the roots of the equation 4x^2 - 2x - 1 = 0. 2) Solving the equation 3x^2 + (p - 2)x - 1 = 0 for p. 3) Solving the equation x^2 - px + 6 = 0 for p when one root is given as 2. 4) Deriving the relationship between the sum and product of the roots p and q, and their coefficients for the general quadratic equation.

1. JumlahdanHasil Kali Akar-AkarPersamaanKuadrat
1. Jika x1dan x2akar-akarpersamaankuadrat 4x2 – 2x – 1 = 0
a. x1 + x2 =
=
=
=
b. x1. x2 =
=
c. (x1 + x2)2 = x12 + 2x1x2 + x22
(x1+ x2)2 = x12 + x22 + 2x1x2
(x1 + x2)2 – 2x1x2 = x12 + x22
Jadi :
x12 + x22 = (x1 + x2)2 – 2x1x2
=
2
–2(
= +
=
d.
+
+
=
=
= .
=
= 2
2. 3x2 + (p − 2)x – 1 = 0
x1 + x2 = 2
− =2
−
=2
−p + 2 = 6
SMK NEGERI 1 TABANAN
1
MATEMATIKA KLS X

2. −p = 6 – 2
p = −4
jadi : 3x2 + (p – 2)x – 1 = 0
3x2 + (−4 −2)x – 1= 0
3x2 – 6x – 1= 0
x2 – 2x − = 0
x2 – 2x =
x2 – 2x (−1)2 = + (−1)2
(x – 1)2 =
(x – 1)2 = +
(x – 1)2 =
(x – 1) = ±√
x–1=√
x1 = 1 + √
3. x2 – px + 6 = 0
atau
x – 1 = −√
x2 = 1 − √
x1 = 2
x1. x2 =
2 .x2 =
x2= 6
x2 = 3
x1 + x2 =
2+3=
5=
5=p
SMK NEGERI 1 TABANAN
2
MATEMATIKA KLS X

3. 4. p + q =
p.q=
(p – q)2 = p2 – 2pq + q2
= p2 + q2 – 2pq
= (p + q)2 – 2pq – 2pq
= (p + q)2 – 4pq
2
=(
=
−
=
−4
−
=
SMK NEGERI 1 TABANAN
3
MATEMATIKA KLS X