Question

Przedstaw trójmiany kwadratowe w postaci iloczynowej : a) x4+2x2-3=0 b)x4-5x2+4=0 c)x4-10x2+9=0 d)x4-13x2+36=0

Answer 1

a)

x4+2x2-3=0

x⁴-x²+3x²-3=0

x²(x²-1)+3(x²-1)=0

(x²+3)(x²-1)=0

(x²+3)(x+1)(x-1)=0

 

b)

x4-5x2+4=0

x⁴-x²-4x²+4=0

x²(x²-1)-4(x²-1)=0

(x²-4)(x²-1)=0

(x+2)(x-2)(x+2)(x-1)=0

 

c)

x4-10x2+9=0

x⁴-x²-9x²+9=0

x²(x²-1)-9(x²-1)=0

(x²-9)(x²-1)=0

(x+3)(x-3)(x+1)(x-1)=0

 

d)

x4-13x2+36=0

x⁴-4x²-9x²+36=0

x²(x²-4)-9(x²-4)=0

(x²-9)(x²-4)=0

(x+3)(x-3)(x+2)(x-2)=0