Question

Jika P dan Q adalah akar akar persamaan kuadrat 3x² -2X-1 = 0 Tentukanlah nilai dari :
a. 1/P + 1/Q
b. P-Q
c. P⁴Q - PQ²
d. P/Q - Q/P

Answer 1

3x² - 2x - 1 = 0
jumlah akar-akar p+q = -b/a = -(-2)/3 = 2/3
hasil kali akar-akar pq = c/a = -1/3

a) 1/p + 1/q = -b/c = -(-2)/-1 = -2
b) p - q = √D/a = √(b² - 4ac)/a = √((-2)²-4(3)(-1))/3 = √(16)/3 = 4/3
c) p²q - pq² = pq(p - q) = -1/3 (4/3) = -4/9
d) p/q - q/p = (p² - q²)/pq = (p+q)(p-q)/pq = (2/3)(4/3)/(-1/3) = - 8/3