Pertanyaan

Persamaan kuadrat 2 x 2 − p x + 1 = 0 dengan p > 0, mempunyai akar-akar α d an β . Jika x 2 − 5 x + q = 0 mempunyai akar-akar α 2 1 d an β 2 1 maka nilai dari q - p adalah....

Persamaan kuadrat $2 x^{2} - p x + 1 = 0$ dengan p > 0, mempunyai akar-akar $α d an β$ . Jika $x^{2} - 5 x + q = 0$ mempunyai akar-akar $\frac{1}{α ^{2}} d an \frac{1}{β ^{2}}$ maka nilai dari q - p adalah....

-2
1
2

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Hitung jumlah dan hasil kali akar-akarnya terlebih dahulu, yaitu:

$U n t u k space p e r s a m a a n space 2 x squared minus p x plus 1 equals 0 comma space d i p e r o l e h space colon alpha plus beta equals p over 2 alpha beta equals 1 half U n t u k space p e r s a m a a n space x squared minus 5 x plus q equals 0 comma space d i p e r o l e h space colon 1 over alpha squared plus 1 over beta squared equals 5 rightwards arrow fraction numerator alpha squared plus beta squared over denominator open parentheses alpha beta close parentheses squared end fraction equals 5 space space space space space space space space space space space space space space space space space space space space space space rightwards arrow fraction numerator open parentheses alpha plus beta close parentheses squared minus 2 alpha beta over denominator open parentheses alpha beta close parentheses squared end fraction equals 5 space space space space space space space space space space space space space space space space space space space space space space rightwards arrow fraction numerator open parentheses p over 2 close parentheses squared minus 2 open parentheses 1 half close parentheses over denominator open parentheses 1 half close parentheses squared end fraction equals 5 space space space space space space space space space space space space space space space space space space space space space space rightwards arrow p squared minus 4 equals 5 space space space space space space space space space space space space space space space space space space space space space space rightwards arrow p squared minus 9 equals 0 space space space space space space space space space space space space space space space space space space space space space space rightwards arrow open parentheses p plus 3 close parentheses open parentheses p minus 3 close parentheses equals 0 space space space space space space space space space space space space space space space space space space space space space space rightwards arrow p equals negative 3 space a t a u space p equals 3 comma space K a r e n a space p greater than 0 comma space m a k a space h a n y a space p equals 3 space y a n g space m e m e n u h i. 1 over alpha squared 1 over beta squared equals q rightwards arrow 1 over open parentheses alpha beta close parentheses squared equals q space space space space space space space space space space space space space space space space space space space rightwards arrow 1 over open parentheses 1 half close parentheses squared equals q space space space space space space space space space space space space space space space space space space space space rightwards arrow 4 equals q J a d i comma space n i l a i space q minus p equals 4 minus 3 equals 1$

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

0.0 (0 rating)

Pertanyaan serupa

[UN 2011] Akar-akar persamaan kuadrat 3 x 2 − x + 9 = 0 adalah x 1 dan x 2 . Nilai dari x 2 x 1 + x 1 x 2 adalah...

0.0

Jawaban terverifikasi

A ka r − aka r p ers amaan x 2 − 12 x + p = 0 a d a l ah x 1 d an x 2 . J ika x 1 − x 2 = 2 , maka ni l ai p = ....

0.0

Jawaban terverifikasi

Persamaan x 2 − a x − ( a + 1 ) = 0 mempunyai akar-akar x 1 > 1 d an x 2 < 1 ketika a bernilai....

0.0

Jawaban terverifikasi

P ers amaan k u a d r a t 2 x 2 − 7 x + 6 = 0 m e m p u n y ai aka r − aka r α d an β . De n g an d e mikian ni l ai d a r i ( α + β ) 2 = ....

0.0

Jawaban terverifikasi

Jika jumlah kuadrat akar-akar real persamaan kuadrat x 2 − x − p = 0 sama dengan kuadrat jumlah kebalikan akar-akar persamaan x 2 − p x − 1 = 0 , maka nilai p adalah ...

0.0

Jawaban terverifikasi