1.1) 4х^2=9
x^2=9/4
x1=√ 9/4=3/2=2,5
x2= - √ 9/4= - 3/2= -2,5
2) 7x^2 - 5x = 0
x(7x-5)=0
x1=0
7x-5=0
7x=5
x2=5/7
3) 2x^2 - 3x +5 = 0
D= (-3)^2 - 4*2*5 = 9 - 40= -31 < 0 => Нет решений
2. 1) x^2 - 7x +10
по т. Виета:
x1+x2 = 7
x1*x2=10 } => x1=2 x2=5
x^2 - 7x +10 = (x - 2)(x -5)
2) 3x^2 - 5x -2
D= (-5)^2 - 4*3*(-2) = 25 + 24= 49
x1 = (5 + 7)/2*3= 12/6=2
x2=(5-7)/2*3= -2/6= - 1/3
3x^2 - 5x -2 = 3(x-2)(x+1/3) = (x-2)(3x+1)