Jawab:
Penjelasan dengan langkah-langkah:
2 akar negatif (kurang dari 0) : x1.x2 > 0, x1+x2 < 0, D > 0
1. x1.x2 > 0
c/a > 0
(p+1)/(p+2) > 0
p < -2 atau p > -1
2. x1+x2 < 0
-b/a < 0
-(-(2p-1))/(p+2) < 0
(2p-1)/(p+2) < 0
-2<p<1/2
3. D > 0
b²-4ac > 0
(-(2p-1))²-4.(p+2).(p+1) > 0
(2p-1)²-4(p²+3p+2) > 0
4p²-4p+1 - 4p²-12p-8 > 0
-16p-7 > 0
16p+7 < 0
p < -7/16
3. (p < -2 ∪ p > -1) ∩ (-2<p<1/2) ∩ (p < -7/16)
batas p yang memenuhi : -1 < p < -7/16
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Jawab:
Penjelasan dengan langkah-langkah:
2 akar negatif (kurang dari 0) : x1.x2 > 0, x1+x2 < 0, D > 0
1. x1.x2 > 0
c/a > 0
(p+1)/(p+2) > 0
p < -2 atau p > -1
2. x1+x2 < 0
-b/a < 0
-(-(2p-1))/(p+2) < 0
(2p-1)/(p+2) < 0
-2<p<1/2
3. D > 0
b²-4ac > 0
(-(2p-1))²-4.(p+2).(p+1) > 0
(2p-1)²-4(p²+3p+2) > 0
4p²-4p+1 - 4p²-12p-8 > 0
-16p-7 > 0
16p+7 < 0
p < -7/16
3. (p < -2 ∪ p > -1) ∩ (-2<p<1/2) ∩ (p < -7/16)
batas p yang memenuhi : -1 < p < -7/16