Составте квадратное уравнение ах+bx+c=0, если известны значения его корней

1) x=-5/6 и x=7

2) x=0,9 и x=-11

3) х=-3/4 и х=1/3

4) х=-0,8 и х=-1/5

1) x = - 5/6 и x = 7

x^2 + px + q = 0

- (x1 + x2) = p

p = - (- 5/6 + 7) = - 6 (1/6)

p = - 6 (1/6)

q = x1*x2

q = (- 5/6) * 7 = - 35/6 = - 5 (5/6)

q = - 5 (5/6)

x^2 - 6 (1/6) x - 5 (5/6) = 0

2) x=0,9 и x=-11

- (x1 + x2) = p

p = - (0,9 - 11) = 1,1

p = 1,1

x1*x2 = q

q = 0,9 * (-11) = - 9,9

q = - 9,9

x^2 + 1,1x - 9,9 = 0

3) х=-3/4 и х=1/3

- (x1 + x2) = p

- (-3/4 + 1/3) = 5/12

p = 5/12

q = x1*x2

q = (- 3/4) * (1/3) = - 1/4

x^2 + 5/12x - 1/4 = 0

4) х=-0,8 и х=-1/5

- (x1 + x2) = p

- (- 0,8 - 0,2) = 1

p = 1

x1*x2 = q

q = (-0,8) * (-0,2) = 0,16

x^2 + x + 0,16 = 0