Question

FUNKCJE KWADRATOWE

1) 3X²+2x=0

2)4x²-9=0

3)x²=4x

4)-x²+7x-10=0

5)9x²=16

6)x²+2x+1=0

7)-x²-6x-9=0

WZORY

Δ=b²-4ac

x₂=-b+√Δ/2a

x₁=-b-√Δ/2a

Answer 1

1]

3x²+2x=0

x(3x+2)=0

x=0 ∨ 3x=-2

x=0 ∨ x=-⅔

2]

4x²-9=0

(2x+3)(2x-3)=0

2x=-3 ∨ 2x=3

x=-1,5 ∨ x=1,5

3]

x²=4x

x²-4x=0

x(x-4)=0

x=0 ∨ x=4

4]

-x²+7x-10=0

Δ=b²-4ac=49-40=9

√Δ=3

x₁=[-b-√Δ]/2a=[-7-3]/-2=5

x₂=[-b+√Δ]/2a=[-7+3]/-2=2

5]

9x²=16

9x²-16=0

(3x+4)(3x-4)=0

3x=-4 ∨ 3x=4

x=-⁴/₃ ∨ x=⁴/₃

6]

x²+2x+1=0

Δ=4-4=0

x₀=-b/2a=-2/2=-1

7]

-x²-6x-9=0

Δ=36-36=0

x₀=-b/2a=6/-2=-3