1) а) 1 и -3, б) 0 и -1/6, в) 0,5 и -3, г) 1 и -1/6
2) а) D = 4^2 - 4*5(-1) = 36, б) D = 6^2 - 4*1*9 = 0, в) D = 0 - 4*3(-4) = 48,
г) D = 4^2 - 4*1*5 = -4
3) а) 2, б) 1, в) 2, г) 0
4) а) (x-2)(x-5) = x^2 - 7x + 10 = 0, б) (x+1)(x-0,8) = x^2 + 0,2x - 0,8 = 0,
в) x(x+3) = x^2 + 3x = 0, г) (x-1/2)(x+1/4) = (2x-1)(4x+1) = 8x^2 - 2x - 1 = 0
д) (x+√2)(x-√2) = x^2 - 2 = 0, е) (x-(1-√2))(x-(1+√2)) = x^2 - 2x - 1 = 0
5) а) -6, 6, б) -1, в) 4, г) 1/49
6) а) x^2 - x = x(x - 1) = 0; x1 = 0; x2 = 1
б) x^2 + 5x + 6 = (x + 2)(x + 3) = 0; x1 = -3; x2 = -2
в) 5x^2 + 8x - 4 = (x + 2)(5x - 2) = 0; x1 = -2; x2 = 2/5
г) x^2 - 6x + 7 = 0; D = 36 - 28 = 8; x1 = (6-√8)/2 = 3-√2; x2 = 3+√2
д) 7x = 4x^2; 4x^2 - 7x = x(4x - 7) = 0; x1 = 0; x2 = 7/4
е) x^2 - 6x + 5 = (x - 1)(x - 5) = 0; x1 = 1; x2 = 5
ж) 5x^2 - 3 = 0; x^2 = 3/5; x1 = -√(3/5); x2 = √(3/5)
з) 2x^2 - x + 3 = 0; D = 1 - 4*2*3 = 1 - 24 < 0; корней нет
7) Решается аналогично 6)
8) а) y^2 - 10y + 25 = (y - 5)^2
б) 9x^2 - 49/144 = (3x - 7/12)(3x + 7/12)
в) y^2 - 5y + 4 = (y - 1)(y - 4)
г) x^2 - x - 6 = (x + 2)(x - 3)
д) 2x^2 - 7 = (√2*x - √7)(√2*x + √7)
е) y^2 + 7y - 8 = (y + 8)(y - 1)
9) а) 8; б) 3
10) Подставляем -3 вместо x
2(-3)^2 - (-3) - m = 2*9 + 3 - m = 21 - m = 0
m = 21