РЕШЕНИЕ:

4x^2​− 29x+45  =0

D = ( – 29)² − 4∙4∙45 = 841 – 720 = 121 = 11²

x₁ = (29+11)/8 = 40/8 = 5

x₁ = (29−11)/8 = 18/8 = 2.25

4x^2​− 29x+45 = 4(x − 5)(x − 2.25)

4x^2​− 29x+45 = 4(x − 5)(x − a)

a = 2.25

Ответ: 2.25

РЕШЕНИЕ:

2x^2​ + 19x+24 =0

D = ( 19)² − 4∙2∙ 24= 361 – 192 = 169 = 13sup]2[/sup]

x₁ = ( –19+13)/4 = 6 /4 = 1.5

x₁ = ( –19−13)/4 = – 32/4= 8

2x^2​ + 19x+ 24 = 2(x + 8)(x− 1..5)

2x^2​ + 19x+ 24=2(x + 8)(x − a)

a = 1.5

Ответ: 1.5

РЕШЕНИЕ:

x²​−2x+1 =0

D = ( – 2)² − 4∙1∙1 = 4 – 4 = 0 = 0²

x₁ = ( 2+0)/2 = 2/2 = 1

x²​−2x+1 = (x – 1)(x−1)

x²​−2x+1=(x−1)(x−a)

a = 1

Ответ: 1

РЕШЕНИЕ:

x²​−9x+14 =0

D = ( – 9)² − 4∙1∙14 = 81 – 56 = 25 = 5²

x₁ = ( 9+5)/2 = 14/2 = 7

x₁ = ( 9−5)/2 = 4/2 = 2

x²​−9x+14 = (x – 7)(x−2)

x²​−9x+14=(x−7)(x−a)

a = 2

Ответ: 2

РЕШЕНИЕ:

x²​−8x+12 =0

D = ( –8)² − 4∙1∙12 = 64 – 48 = 16 = 4²

x₁ = ( 8+4)/2 = 12/2 = 6

x₁ = ( 8−4)/2 = 4/2 = 2

x²​−8x+12 = (x – 2)(x−6)

x²​−8x+12=(x−2)(x−a)

a = 6

Ответ: 6

РЕШЕНИЕ:

5x²​ + 33x+40  =0

D = ( 33)² − 4∙5∙ 40 = 1089 – 800 = 289 = 17²

x₁ = ( – 33+17)/10 = – 16 /10 = – 1.6

x₁ = ( – 33 −17)/10 = – 50/10= – 5

5x²​+33x+40 = 5(x + 5)(x − ( – 1.6))

5x²​+33x+40 = 5(x + 5)(x − a)

a = – 1.6

Ответ: –1.6