Question

A) X^2-7x+12 D) X^2-2x-63

Answer 1

А) х²-7х+12=0 
а=1; b= -7; с=12 
D=b²-4ac=(-7)²-4*1*12=49-48=1 
√D=√1=1 
x₁ = (-b-√D)/2a = (7-1)/2 = 3 
x₂ = (-b+√D)/2a = (7+1)/2 = 4 

d) D=4+252=256
√D=16 
x₁ = (2-16)/2 = -7 
x₂ = (2+16)/2 = 9

Answer 2

Factorization of X^2-7x+12: We need to find two numbers that add up to -7 and multiply to 12. These numbers are -3 and -4. Therefore, we can factor X^2-7x+12 as (X-3)(X-4).

Factorization of X^2-2x-63: We need to find two numbers that add up to -2 and multiply to -63. These numbers are 7 and -9. Therefore, we can factor X^2-2x-63 as (X+7)(X-9).