Question

va rog ajutati ma dau coroana!!!!

Answer 1

Forma generala a ecuatiei de gradul al doilea este : a·x²+b·x+c=0

Calculam delta: Δ=b²-4·a·c

Daca Δ<0, ecuatia nu are solutii reale.

Daca Δ≥0 ecuatia are 2 solutii reale x₁,₂ = (-b ± √Δ)/2a

 daca Δ=0 ⇒x₁=x₂=-b/2a

1) 2x²-5x+3=0

Δ=(-5)²-4·2·3 = 25-24 = 1

Δ = 1 >0

x₁,₂ = [-(-5)±√1]/2·2 = (5 ± 1)/4

⇒ x₁ = (5 + 1)/4 = 6/4 =3/2

x₂ = (5 - 1)/4 = 4/4 =1

deci sulutiile ecuatiei sunt :  x₁ = 3/2, x₂ = 1

10) x²+x+15=0

Δ=1²-4·1·15 = 1 - 60 = -59 <0

Δ<0 ⇒ ecuatia nu are solutii reale.

In mod asemanator se rezolva toate celelalte ecuatii

Answer 2

$\it 9)\ -x^2+x-5=0|_{\cdot(-1)} \Rightarrow x^2-x+5=0\\ \\ \Delta =1-20=-19<0 \Rightarrow x_{1,2}\not\in\mathbb{R}\\ \\ 4)\ 2x^2-7x+6=0 \Rightarrow 2x^2-3x-4x+6=0 \Rightarrow x(2x-3)-2(2x-3)=0 \Rightarrow \\ \\ \\ \Rightarrow (2x-3)(x-2)=0 \Rightarrow \begin{cases} \it 2x-3=0 \Rightarrow x_1=\dfrac{3}{2}=1,5\\ \\ \it x-2=0 \Rightarrow x_2=2\end{cases}$