Question

POMOCY???????????!!???​

Answer 1

Wzór ogólny funkcji kwadratowej ma postać:

ax² + bx + c = 0

A)

8x - 2x(3x - 1) = 2x² + 3

8x - 6x² + 2x = 2x² + 3

8x - 6x² + 2x - 2x² - 3 = 0

-8x² + 10x - 3 = 0

Δ = b² - 4ac = 10² - 4×(-8)×(-3) = 100 - 96 = 4

√Δ = 2

x1 = (-b-√Δ)/2a = (-10-2)/(-16) = 0,75

x2 = (-b+√Δ)/2a = (-10+2)/(-16) = 0,5

C)

(2x - 4)(2x + 4) = (3x - 1)² - 16

(2x)² - 4² = (3x)² - 2×3x×1 + 1² - 16

4x² - 16 = 9x² - 6x - 15

4x² - 16 - 9x² + 6x + 15 = 0

-5x² + 6x - 1 = 0

Δ = b² - 4ac = 6² - 4×(-5)×(-1) = 36 - 20 = 16

√Δ = 4

x1 = (-b-√Δ)/2a = (-6-4)/(-10) = 1

x2 = (-b+√Δ)/2a = (-6+4)/(-10) = 0,2

E)

(x² - 3x + 1)(x + 2) = x³ - 2x - 1

x³ - 3x² + x + 2x² - 6x + 2 = x³ - 2x - 1

x³ - 3x² + x + 2x² - 6x + 2 - x³ + 2x + 1 = 0

-x² - 3x + 3 = 0

Δ = b² - 4ac = (-3)² - 4×(-1)×(3) = 9 + 12 = 21

√Δ = √21

x1 = (-b-√Δ)/2a = (3 - √21)/(-2) = -(3 - √21)/2

x2 = (-b+√Δ)/2a = (3+√21)/(-2) = -(3+√21)/2