Question

Diketahui bahwa p dan q adalah akar-akar dari persamaan kuadrat x^2 + 3x + 4
Tentukan :
A. p + q
B. p . q
C. p^2 + q^2
D. 1/p + 1/q
E. p/q + q/p

Answer 1

Verified answer

X² + 3x + 4
a = 1 , b = 3 , c = 4

a) p + q = - b/a = - 3/1 = - 3

b) p • q = c/a = 4/1 = 4

c) p² + q²
= ( p + q )² - 2pq
= ( - 3)² - 2(4)
= 9 - 8
= 1

d) 1/p + 1/q
= q + p
-----------
p • q

= - 3
---------
4

= - ¾


e) p/q + q/p

= p² + q²
---------------
pq

= ( p + q )² - 2pq
--------------------------
pq

= ( - 3 )² - 2(4 )
--------------------
4

= 9 - 8
-----------
4

= ¼