РЕШЕНИЕ:

4 x ² ​+15x−4=0

D = ( 15)² − 4∙4∙(−4) = 225 + 64 = 289 = 17²

x₁ = (−15+17)/8 = 2/8 = 0.25

x₁ = (−15−17)/8 = −32/8 = −4

4 x ² ​+15x−4=4 (x+4)(x−0.25)

4 x ² ​+15x−4=4( x+4 )( x − a )

a = 0.25

Ответ: 0.25

РЕШЕНИЕ:

x^2​+8x+12=0

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

x₁ = (−8+4)/2 = – 4/2 = – 2

x₁ = (−8−4)/2 = −12/2 = −6

x^2​+8x+12 = (x+2)(x−( – 6))

x^2​+8x+12=(x+2)(x−a)

a = – 6

Ответ: – 6

РЕШЕНИЕ:

2x^2​ + 19x + 42 =0

D = ( 19)² − 4∙2∙ 42 = 361 – 336 = 25 = 5²

x₁ = ( –19+5)/4 = – 14 /4 = – 3.5

x₁ = ( –19−5)/4 = – 24/4= 6

2x^2​ +  19x + 42 = 2(x + 6 )(x− ( – 3.5))

2x^2​ +  19x + 42 =2(x  + 6 )(x − a)

a = ( – 3.5)

Ответ: – 3.5

РЕШЕНИЕ:

2x^2​ – 5x + 2 =0

D = ( – 5)² − 4∙2∙ 2 = 25 – 16 = 9 = 3²

x₁ = ( 5+3)/4 = 8 /4 = 2

x₁ = ( 5−3)/4 = 2/4= 0.5

2x^2​ – 5x + 2 = 2(x – 2 )(x− 0.5)

2x^2​ – 5x + 2=2(x  – 2 )(x − a)

a = 0.5

Ответ: 0.5

РЕШЕНИЕ:

x²​+6x−27 =0

D = ( 6)² − 4∙1∙( – 27) = 36 + 108 = 144 = 12²

x₁ = (−6+12)/2 = 6/2 = 3

x₁ = (−6−12)/2 = −18/2 = −9

x²​+6x−27 = (x+9)(x−3)

x²​+6x−27=(x+9)(x−a)

a = 3

Ответ: 3

РЕШЕНИЕ:

x²​+12x+32 =0

D = (12)² − 4∙1∙32 = 144+ 128 = 16 = 4²

x₁ = (−12+4)/2 = – 8/2 = – 4

x₁ = (−12−4)/2 = −16/2 = −8

x²​+12x+32 = (x+8)(x−( – 4))

x²​+12x+32=(x+8)(x−a)

a = – 4

Ответ: – 4