Question

Jika suku banyak x⁴ - 7x² + 1 dapat difaktorkan menjadi (x² + ax + b)(x² + cx + d) maka nilai a+b+c+d = ...

a. -4
b. -2
c. 0
d. 1
e. 2

Answer 1

Verified answer

(x^2 + ax + b)(x^2 + cx + d)
= x^4 + cx^3 + dx^2 + ax^3 + acx^2 + adx + bx^2 + bcx + bd
= x^4 + (c + a)x^3 + (d + ac + b)x^2 + (ad + bc)x + bd
= x^4 - 7x^2 + 1

Koefisien x^3
c + a = 0 => a = -c

Koefisien x^2
d + ac + b = -7

Koefisien x
ad + bc = 0 => -cd + bc = 0 => bc = cd => b = d

Konstanta
bd = 1 => d.d = 1 => d = 1

b = d = 1

a + b + c + d = -c + 1 + c + 1 = 2

Answer 2

Verified answer

Uraikan pemfaktorannya menjadi
x^4+(a+c)x^3+(b+ac+d)x^2+(ad+bc)x+bd = x^4-7x^2+1
Bandingkan koefisien dari variabel yg bersesuaian:
a+c=0 sama saja dgn a = -c
b+ac+d=-7
ad+bc=0 => bc-cd = 0 => bc = cd => b = d
bd=1
akibatnya b = 1 dan d = 1,
sehingga a+b+c+d=(-c)+1+c+1=2.
(Jawaban E)