SPMB 2007 kode 541 Persamaan kuadrat 4x² + p = -1 mempunyai akar x1 dan x2 , jika x1 = 1/2, maka p(x1² + x2²) = ... a) -3/2 b) -5/4 c) -1 d) -1/2 e) 6

Jika salah satu akarnya -1/2
Maka substitusikan =

4x² + p = -1
4(1/2)² + p = -1
4(1/4)+p = -1
1 + p = -1
p = -2

Sehingga persamaannya :
4x² + (-2) = -1
4x² - 2 = -1
4x² - 1 = 0
(2x+1)(2x-1) = 0
X1 = 1/2 , x2 = -1/2

Jadi,
p( (x1²)+(x2²) )
= -2( (1/2)² + (-1/2)² )
= -2 ( (1/4) + (1/4) )
= -2 x (1/2)
= -1

•subtitusi x1=1/2 ke persamaan kuadrat
4x²+p=-1
4(1/2)²+p=-1
p= -2
•kemudian subtitusi p=-2 ke persamaan kuadrat
4x²+p=-1
4x²+(-2)=-1
4x²=1
x²=1/4
x=±1/2
x1 = 1/2, X2=-1/2
•p(x1²-x2²)
(-2)((1/2)²+(-1/2)²)
-2(1/4+1/4)=-1

jawabannya -1 (C)